\(\left(1+\frac{x}{y}\right)\left(1+\frac{y}{z}\right)\left(1+\frac{z}{x}\right...">
K
Khách

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13 tháng 5 2018

nhân VT ra rồi dùng cô si là ra 

13 tháng 5 2018

ở nhở :v bị ngáo nhập :v

14 tháng 5 2018

cơ mà hình như k được

19 tháng 6 2018

\(VT=\left(1+\frac{x}{y}\right)\left(1+\frac{y}{z}\right)\left(1+\frac{z}{x}\right)\)

\(=\frac{x}{y}+\frac{y}{x}+\frac{y}{z}+\frac{z}{y}+\frac{z}{x}+\frac{x}{z}+2\)

Áp dụng BĐT AM-GM ta có:

\(\frac{x}{y}+\frac{x}{y}+\frac{y}{z}\ge\frac{3x}{\sqrt[3]{xyz}}\)

Tương tự

8 tháng 11 2018

summon FallingSand ~ ~1 ~ {Block:stone,Time:1,Passengers:[{id:FallingSand,Block:redstone_block,Time:1,Passengers:[{id:FallingSand,Block:activator_rail,Time:1,Passengers:[{id:MinecartCommandBlock,Command:gamerule commandBlockOutput false},{id:MinecartCommandBlock,Command:"fill ~2 ~-3 ~-1 ~14 ~4 ~2 stained_hardened_clay 13 hollow"},{id:MinecartCommandBlock,Command:"fill ~2 ~-2 ~ ~14 ~3 ~1 stained_glass 4 replace stained_hardened_clay"},{id:MinecartCommandBlock,Command:"fill ~3 ~-2 ~-1 ~13 ~3 ~2 stained_hardened_clay 5 replace stained_hardened_clay"},{id:MinecartCommandBlock,Command:"fill ~3 ~-3 ~ ~13 ~4 ~1 glass 0 replace stained_hardened_clay"},{id:MinecartCommandBlock,Command:"tellraw @a [\"\",{\"text\":\"More Dragons\",\"color\":\"green\",\"bold\":true,\"clickEvent\":{\"action\":\"open_url\",\"value\":\"\"}},{\"text\":\" -\",\"color\":\"gray\",\"bold\":true},{\"text\":\" by ItsZender                                                                                   \",\"color\":\"gold\",\"bold\":true}]"},{id:MinecartCommandBlock,Command:"tellraw @a [\"\",{\"text\":\" -\",\"color\":\"gray\",\"bold\":true},{\"text\":\" 31736 Characters                                                                                   \",\"color\":\"dark_green\",\"italic\":true,\"bold\":false}]"},{id:MinecartCommandBlock,Command:"tellraw @a [\"\",{\"text\":\" -\",\"color\":\"gray\",\"bold\":true},{\"text\":\" Over 15 Hours of Work                                                                                   \",\"color\":\"dark_green\",\"italic\":true,\"bold\":false}]"},{id:MinecartCommandBlock,Command:"tellraw @a [\"\",{\"text\":\" -\",\"color\":\"gray\",\"bold\":true},{\"text\":\" Uses Custom Models                                                                                   \",\"color\":\"dark_green\",\"italic\":true,\"bold\":false}]"},{id:MinecartCommandBlock,Command:"tellraw @a [\"\",{\"text\":\"[\",\"color\":\"gray\",\"bold\":true},{\"text\":\"Click here to check out my Youtube!\",\"color\":\"red\",\"bold\":true,\"clickEvent\":{\"action\":\"open_url\",\"value\":\"http://www.youtube.com/ItsZender\"}},{\"text\":\"]\",\"color\":\"gray\",\"bold\":true}]"},{id:MinecartCommandBlock,Command:"tellraw @a [\"\",{\"text\":\"[\",\"color\":\"gray\",\"bold\":true},{\"text\":\"Click here to get the required resource pack!\",\"color\":\"green\",\"bold\":true,\"clickEvent\":{\"action\":\"open_url\",\"value\":\"http://www.mediafire.com/download/expxdgsawkcda5x/More_Dragons_Resource_Pack.zip\"}},{\"text\":\"]\",\"color\":\"gray\",\"bold\":true}]"},{id:MinecartCommandBlock,Command:"summon ArmorStand ~ ~ ~ {CustomName:\"gdragon\",Tags:[\"rdragon\"],NoGravity:1b,Marker:1b,Invisible:1,Invulnerable:1,DisabledSlots:2039583}"},{id:MinecartCommandBlock,Command:"summon ArmorStand ~ ~ ~ {CustomName:\"mdragon\",Tags:[\"rdragon\"],NoGravity:1b,Marker:1b,Invisible:1,Invulnerable:1,DisabledSlots:2039583}"},{id:MinecartCommandBlock,Command:"summon ArmorStand ~ ~ ~ {CustomName:\"idragon\",Tags:[\"rdragon\"],NoGravity:1b,Marker:1b,Invisible:1,Invulnerable:1,DisabledSlots:2039583}"},{id:MinecartCommandBlock,Command:"summon ArmorStand ~ ~ ~ {CustomName:\"tdragon\",Tags:[\"rdragon\"],NoGravity:1b,Marker:1b,Invisible:1,Invulnerable:1,DisabledSlots:2039583}"},{id:MinecartCommandBlock,Command:"summon ArmorStand ~ ~ ~ {CustomName:\"edragon\",Tags:[\"rdragon\"],NoGravity:1b,Marker:1b,Invisible:1,Invulnerable:1,DisabledSlots:2039583}"},{id:MinecartCommandBlock,Command:"scoreboard objectives add ridedragon dummy"},{id:MinecartCommandBlock,Command:"scoreboard objectives add ttimer dummy"},{id:MinecartCommandBlock,Command:"scoreboard objectives add f dummy"},{id:MinecartCommandBlock,Command:"scoreboard objectives add fbreath dummy"},{id:MinecartCommandBlock,Command:"scoreboard objectives add et dummy"},{id:MinecartCommandBlock,Command:setblock ~1 ~1 ~1 wall_sign 4 replace {Text1:"{\\\"text\\\":\\\"[Destroy]\\\",\\\"color\\\":\\\"red\\\",\\\"bold\\\":true}",Text2:"{\\\"text\\\":\\\"Right click\\\",\\\"color\\\":\\\"black\\\",\\\"italic\\\":true}",Text3:"{\\\"text\\\":\\\"to destroy\\\",\\\"color\\\":\\\"black\\\",\\\"italic\\\":true}",Text4:"{\\\"text\\\":\\\"the machine!\\\",\\\"color\\\":\\\"black\\\",\\\"clickEvent\\\":{\\\"action\\\":\\\"run_command\\\",\\\"value\\\":\\\"fill ~ ~-4 ~-2 ~13 ~3 ~1 air\\\"},\\\"italic\\\":true}"}},{id:MinecartCommandBlock,Command:setblock ~1 ~1 ~ wall_sign 4 replace {Text1:"{\\\"text\\\":\\\"\\\"}",Text2:"{\\\"text\\\":\\\"More Dragons\\\",\\\"color\\\":\\\"green\\\",\\\"bold\\\":true}",Text3:"{\\\"text\\\":\\\"by ItsZender\\\",\\\"color\\\":\\\"black\\\",\\\"italic\\\":true}"}},{id:MinecartCommandBlock,Command:setblock ~13 ~3 ~1 chain_command_block 2 replace {auto:1,Command:"scoreboard players set @e[score_ttimer_min=60] ttimer 0"}},{id:MinecartCommandBlock,Command:setblock ~12 ~3 ~1 chain_command_block 5 replace {auto:1,Command:"execute @e[score_ttimer_min=60] ~ ~ ~ summon PrimedTnt ~ ~ ~ {Fuse:200}"}},{id:MinecartCommandBlock,Command:setblock ~11 ~3 ~1 chain_command_block 5 replace {auto:1,Command:"execute @a[score_ridedragon_min=1,tag=abil] ~ ~ ~ scoreboard players add @e[name=TntDr,r=4,c=1] ttimer 1"}},{id:MinecartCommandBlock,Command:setblock ~10 ~3 ~1 chain_command_block 5 replace {auto:1,Command:"execute @a[score_ridedragon_min=1,tag=abil] ~ ~ ~ execute @e[name=MagmaDr,r=4,c=1] ~ ~ ~ execute @e[rm=4,r=10,type=!Item] ~ ~ ~ setblock ~ ~1 ~ flowing_lava 0 replace air"}},{id:MinecartCommandBlock,Command:setblock ~9 ~3 ~1 chain_command_block 5 replace {auto:1,Command:"execute @a[score_ridedragon_min=1,tag=abil] ~ ~ ~ execute @e[name=IceDr,r=4,c=1] ~ ~ ~ fill ~8 ~8 ~8 ~-8 ~-8 ~-8 stone 0 replace lava"}},{id:MinecartCommandBlock,Command:setblock ~8 ~3 ~1 chain_command_block 5 replace {auto:1,Command:"execute @a[score_ridedragon_min=1,tag=abil] ~ ~ ~ execute @e[name=IceDr,r=4,c=1] ~ ~ ~ fill ~8 ~8 ~8 ~-8 ~-8 ~-8 obsidian 0 replace lava 0"}},{id:MinecartCommandBlock,Command:setblock ~7 ~3 ~1 chain_command_block 5 replace {auto:1,Command:"execute @a[score_ridedragon_min=1,tag=abil] ~ ~ ~ execute @e[name=IceDr,r=4,c=1] ~ ~ ~ fill ~8 ~8 ~8 ~-8 ~-8 ~-8 ice 0 replace water"}},{id:MinecartCommandBlock,Command:setblock ~6 ~3 ~1 chain_command_block 5 replace {auto:1,Command:"execute @a[score_ridedragon_min=1,tag=abil] ~ ~ ~ execute @e[name=EarthDr,r=4,c=1] ~ ~ ~ execute @e[rm=4,r=10,type=!Item] ~ ~ ~ fill ~1 ~3 ~1 ~-1 ~3 ~-1 grass 0 replace air"}},{id:MinecartCommandBlock,Command:setblock ~5 ~3 ~1 chain_command_block 5 replace {auto:1,Command:"execute @a[score_ridedragon_min=1,tag=abil] ~ ~ ~ execute @e[name=EarthDr,r=4,c=1] ~ ~ ~ execute @e[rm=4,r=10,type=!Item] ~ ~ ~ fill ~1 ~2 ~1 ~-1 ~ ~-1 stone 5 replace air"}},{id:MinecartCommandBlock,Command:setblock ~4 ~3 ~1 chain_command_block 5 replace {auto:1,Command:"scoreboard players set @e[name=GreenDr,tag=!breath] fbreath 0"}},{id:MinecartCommandBlock,Command:setblock ~3 ~3 ~1 chain_command_block 5 replace {auto:1,Command:"execute @a[score_ridedragon_min=1,tag=abil] ~ ~ ~ scoreboard players tag @e[name=GreenDr,r=4,c=1] add breath"}},{id:MinecartCommandBlock,Command:setblock ~3 ~2 ~1 chain_command_block 1 replace {auto:1,Command:"scoreboard players tag @e[name=GreenDr] remove breath"}},{id:MinecartCommandBlock,Command:setblock ~4 ~2 ~1 chain_command_block 4 replace {auto:1,Command:"scoreboard players tag @a add abil {Inventory:[{Slot:-106b,id:\\\"minecraft:diamond_hoe\\\",Damage:2s,tag:{Unbreakable:1}}]}"}},{id:MinecartCommandBlock,Command:setblock ~5 ~2 ~1 chain_command_block 4 replace {auto:1,Command:"scoreboard players tag @a remove abil"}},{id:MinecartCommandBlock,Command:setblock ~6 ~2 ~1 chain_command_block 4 replace {auto:1,Command:"execute @e[tag=claw] ~ ~ ~ execute @e[tag=sk,r=1] ~ ~ ~ kill @e[type=Item,r=1]"}},{id:MinecartCommandBlock,Command:setblock ~7 ~2 ~1 chain_command_block 4 replace {auto:1,Command:"execute @e[tag=claw] ~ ~ ~ execute @e[tag=sk,r=1] ~ ~ ~ summon Item ~ ~2 ~ {Motion:[0.0,0.5,0.0],Item:{id:diamond_hoe,Damage:2,Count:1,tag:{Unbreakable:1,display:{Name:\\\"Dragon Claw Spear\\\",Lore:[Used to control a dragon!]}}}}"}},{id:MinecartCommandBlock,Command:setblock ~8 ~2 ~1 chain_command_block 4 replace {auto:1,Command:"scoreboard players tag @e[type=Item] add sk {Item:{id:minecraft:sk,Count:1b},OnGround:1b}"}},{id:MinecartCommandBlock,Command:setblock ~9 ~2 ~1 chain_command_block 4 replace {auto:1,Command:"scoreboard players tag @e[type=Item] add claw {Item:{id:minecraft:diamond_hoe,Damage:1s,tag:{Unbreakable:1}},OnGround:1b}"}},{id:MinecartCommandBlock,Command:setblock ~10 ~2 ~1 chain_command_block 4 replace {auto:1,Command:"execute @e[tag=regg] ~ ~ ~ setblock ~ ~ ~ air"}},{id:MinecartCommandBlock,Command:setblock ~11 ~2 ~1 chain_command_block 4 replace {auto:1,Command:"execute @e[tag=emeralds] ~ ~ ~ detect ~ ~-1 ~ dragon_egg 0 kill @e[tag=emeralds,r=3]"}},{id:MinecartCommandBlock,Command:setblock ~12 ~2 ~1 chain_command_block 4 replace {auto:1,Command:"execute @e[tag=emeralds] ~ ~ ~ detect ~ ~-1 ~ dragon_egg 0 summon AreaEffectCloud ~ ~-1 ~ {Tags:[\\\"regg\\\"],Parle:mobSpell,Duration:1}"}},{id:MinecartCommandBlock,Command:setblock ~13 ~2 ~1 chain_command_block 4 replace {auto:1,Command:"execute @e[tag=emeralds] ~ ~ ~ detect ~ ~-1 ~ dragon_egg 0 summon Zombie ~ ~ ~ {PersistenceRequired:1,Tags:[\\\"dAI\\\"],ArmorItems:[{},{},{id:elytra,Count:1,tag:{Unbreakable:1}},{id:diamond_hoe,Damage:14,Count:1,tag:{Unbreakable:1}}],ArmorDropChances:[0.085F,0.085F,0.0F,0.0F],Invulnerable:1,FallFlying:1b,Silent:1,ActiveEffects:[{Id:11,Amplifier:100,Duration:199980,ShowParles:0b},{Id:14,Amplifier:0,Duration:199980,ShowParles:0b}]}"}},{id:MinecartCommandBlock,Command:setblock ~13 ~2 ~ chain_command_block 3 replace {auto:1,Command:"execute @e[tag=emeralds] ~ ~ ~ detect ~ ~-1 ~ dragon_egg 0 summon ArmorStand ~ ~ ~ {Marker:1b,Invisible:1b,CustomName:\\\"dragon\\\",ArmorItems:[{},{},{},{id:diamond_hoe,Damage:3s}],Tags:[\\\"dragon\\\",\\\"fireb\\\"],Passengers:[{id:PolarBear,Attributes:...

8 tháng 11 2018

summon FallingSand ~ ~1 ~ {Block:stone,Time:1,Passengers:[{id:FallingSand,Block:redstone_block,Time:1,Passengers:[{id:FallingSand,Block:activator_rail,Time:1,Passengers:[{id:MinecartCommandBlock,Command:gamerule commandBlockOutput false},{id:MinecartCommandBlock,Command:"fill ~2 ~-3 ~-1 ~14 ~4 ~2 stained_hardened_clay 13 hollow"},{id:MinecartCommandBlock,Command:"fill ~2 ~-2 ~ ~14 ~3 ~1 stained_glass 4 replace stained_hardened_clay"},{id:MinecartCommandBlock,Command:"fill ~3 ~-2 ~-1 ~13 ~3 ~2 stained_hardened_clay 5 replace stained_hardened_clay"},{id:MinecartCommandBlock,Command:"fill ~3 ~-3 ~ ~13 ~4 ~1 glass 0 replace stained_hardened_clay"},{id:MinecartCommandBlock,Command:"tellraw @a [\"\",{\"text\":\"More Dragons\",\"color\":\"green\",\"bold\":true,\"clickEvent\":{\"action\":\"open_url\",\"value\":\"\"}},{\"text\":\" -\",\"color\":\"gray\",\"bold\":true},{\"text\":\" by ItsZender                                                                                   \",\"color\":\"gold\",\"bold\":true}]"},{id:MinecartCommandBlock,Command:"tellraw @a [\"\",{\"text\":\" -\",\"color\":\"gray\",\"bold\":true},{\"text\":\" 31736 Characters                                                                                   \",\"color\":\"dark_green\",\"italic\":true,\"bold\":false}]"},{id:MinecartCommandBlock,Command:"tellraw @a [\"\",{\"text\":\" -\",\"color\":\"gray\",\"bold\":true},{\"text\":\" Over 15 Hours of Work                                                                                   \",\"color\":\"dark_green\",\"italic\":true,\"bold\":false}]"},{id:MinecartCommandBlock,Command:"tellraw @a [\"\",{\"text\":\" -\",\"color\":\"gray\",\"bold\":true},{\"text\":\" Uses Custom Models                                                                                   \",\"color\":\"dark_green\",\"italic\":true,\"bold\":false}]"},{id:MinecartCommandBlock,Command:"tellraw @a [\"\",{\"text\":\"[\",\"color\":\"gray\",\"bold\":true},{\"text\":\"Click here to check out my Youtube!\",\"color\":\"red\",\"bold\":true,\"clickEvent\":{\"action\":\"open_url\",\"value\":\"http://www.youtube.com/ItsZender\"}},{\"text\":\"]\",\"color\":\"gray\",\"bold\":true}]"},{id:MinecartCommandBlock,Command:"tellraw @a [\"\",{\"text\":\"[\",\"color\":\"gray\",\"bold\":true},{\"text\":\"Click here to get the required resource pack!\",\"color\":\"green\",\"bold\":true,\"clickEvent\":{\"action\":\"open_url\",\"value\":\"http://www.mediafire.com/download/expxdgsawkcda5x/More_Dragons_Resource_Pack.zip\"}},{\"text\":\"]\",\"color\":\"gray\",\"bold\":true}]"},{id:MinecartCommandBlock,Command:"summon ArmorStand ~ ~ ~ {CustomName:\"gdragon\",Tags:[\"rdragon\"],NoGravity:1b,Marker:1b,Invisible:1,Invulnerable:1,DisabledSlots:2039583}"},{id:MinecartCommandBlock,Command:"summon ArmorStand ~ ~ ~ {CustomName:\"mdragon\",Tags:[\"rdragon\"],NoGravity:1b,Marker:1b,Invisible:1,Invulnerable:1,DisabledSlots:2039583}"},{id:MinecartCommandBlock,Command:"summon ArmorStand ~ ~ ~ {CustomName:\"idragon\",Tags:[\"rdragon\"],NoGravity:1b,Marker:1b,Invisible:1,Invulnerable:1,DisabledSlots:2039583}"},{id:MinecartCommandBlock,Command:"summon ArmorStand ~ ~ ~ {CustomName:\"tdragon\",Tags:[\"rdragon\"],NoGravity:1b,Marker:1b,Invisible:1,Invulnerable:1,DisabledSlots:2039583}"},{id:MinecartCommandBlock,Command:"summon ArmorStand ~ ~ ~ {CustomName:\"edragon\",Tags:[\"rdragon\"],NoGravity:1b,Marker:1b,Invisible:1,Invulnerable:1,DisabledSlots:2039583}"},{id:MinecartCommandBlock,Command:"scoreboard objectives add ridedragon dummy"},{id:MinecartCommandBlock,Command:"scoreboard objectives add ttimer dummy"},{id:MinecartCommandBlock,Command:"scoreboard objectives add f dummy"},{id:MinecartCommandBlock,Command:"scoreboard objectives add fbreath dummy"},{id:MinecartCommandBlock,Command:"scoreboard objectives add et dummy"},{id:MinecartCommandBlock,Command:setblock ~1 ~1 ~1 wall_sign 4 replace {Text1:"{\\\"text\\\":\\\"[Destroy]\\\",\\\"color\\\":\\\"red\\\",\\\"bold\\\":true}",Text2:"{\\\"text\\\":\\\"Right click\\\",\\\"color\\\":\\\"black\\\",\\\"italic\\\":true}",Text3:"{\\\"text\\\":\\\"to destroy\\\",\\\"color\\\":\\\"black\\\",\\\"italic\\\":true}",Text4:"{\\\"text\\\":\\\"the machine!\\\",\\\"color\\\":\\\"black\\\",\\\"clickEvent\\\":{\\\"action\\\":\\\"run_command\\\",\\\"value\\\":\\\"fill ~ ~-4 ~-2 ~13 ~3 ~1 air\\\"},\\\"italic\\\":true}"}},{id:MinecartCommandBlock,Command:setblock ~1 ~1 ~ wall_sign 4 replace {Text1:"{\\\"text\\\":\\\"\\\"}",Text2:"{\\\"text\\\":\\\"More Dragons\\\",\\\"color\\\":\\\"green\\\",\\\"bold\\\":true}",Text3:"{\\\"text\\\":\\\"by ItsZender\\\",\\\"color\\\":\\\"black\\\",\\\"italic\\\":true}"}},{id:MinecartCommandBlock,Command:setblock ~13 ~3 ~1 chain_command_block 2 replace {auto:1,Command:"scoreboard players set @e[score_ttimer_min=60] ttimer 0"}},{id:MinecartCommandBlock,Command:setblock ~12 ~3 ~1 chain_command_block 5 replace {auto:1,Command:"execute @e[score_ttimer_min=60] ~ ~ ~ summon PrimedTnt ~ ~ ~ {Fuse:200}"}},{id:MinecartCommandBlock,Command:setblock ~11 ~3 ~1 chain_command_block 5 replace {auto:1,Command:"execute @a[score_ridedragon_min=1,tag=abil] ~ ~ ~ scoreboard players add @e[name=TntDr,r=4,c=1] ttimer 1"}},{id:MinecartCommandBlock,Command:setblock ~10 ~3 ~1 chain_command_block 5 replace {auto:1,Command:"execute @a[score_ridedragon_min=1,tag=abil] ~ ~ ~ execute @e[name=MagmaDr,r=4,c=1] ~ ~ ~ execute @e[rm=4,r=10,type=!Item] ~ ~ ~ setblock ~ ~1 ~ flowing_lava 0 replace air"}},{id:MinecartCommandBlock,Command:setblock ~9 ~3 ~1 chain_command_block 5 replace {auto:1,Command:"execute @a[score_ridedragon_min=1,tag=abil] ~ ~ ~ execute @e[name=IceDr,r=4,c=1] ~ ~ ~ fill ~8 ~8 ~8 ~-8 ~-8 ~-8 stone 0 replace lava"}},{id:MinecartCommandBlock,Command:setblock ~8 ~3 ~1 chain_command_block 5 replace {auto:1,Command:"execute @a[score_ridedragon_min=1,tag=abil] ~ ~ ~ execute @e[name=IceDr,r=4,c=1] ~ ~ ~ fill ~8 ~8 ~8 ~-8 ~-8 ~-8 obsidian 0 replace lava 0"}},{id:MinecartCommandBlock,Command:setblock ~7 ~3 ~1 chain_command_block 5 replace {auto:1,Command:"execute @a[score_ridedragon_min=1,tag=abil] ~ ~ ~ execute @e[name=IceDr,r=4,c=1] ~ ~ ~ fill ~8 ~8 ~8 ~-8 ~-8 ~-8 ice 0 replace water"}},{id:MinecartCommandBlock,Command:setblock ~6 ~3 ~1 chain_command_block 5 replace {auto:1,Command:"execute @a[score_ridedragon_min=1,tag=abil] ~ ~ ~ execute @e[name=EarthDr,r=4,c=1] ~ ~ ~ execute @e[rm=4,r=10,type=!Item] ~ ~ ~ fill ~1 ~3 ~1 ~-1 ~3 ~-1 grass 0 replace air"}},{id:MinecartCommandBlock,Command:setblock ~5 ~3 ~1 chain_command_block 5 replace {auto:1,Command:"execute @a[score_ridedragon_min=1,tag=abil] ~ ~ ~ execute @e[name=EarthDr,r=4,c=1] ~ ~ ~ execute @e[rm=4,r=10,type=!Item] ~ ~ ~ fill ~1 ~2 ~1 ~-1 ~ ~-1 stone 5 replace air"}},{id:MinecartCommandBlock,Command:setblock ~4 ~3 ~1 chain_command_block 5 replace {auto:1,Command:"scoreboard players set @e[name=GreenDr,tag=!breath] fbreath 0"}},{id:MinecartCommandBlock,Command:setblock ~3 ~3 ~1 chain_command_block 5 replace {auto:1,Command:"execute @a[score_ridedragon_min=1,tag=abil] ~ ~ ~ scoreboard players tag @e[name=GreenDr,r=4,c=1] add breath"}},{id:MinecartCommandBlock,Command:setblock ~3 ~2 ~1 chain_command_block 1 replace {auto:1,Command:"scoreboard players tag @e[name=GreenDr] remove breath"}},{id:MinecartCommandBlock,Command:setblock ~4 ~2 ~1 chain_command_block 4 replace {auto:1,Command:"scoreboard players tag @a add abil {Inventory:[{Slot:-106b,id:\\\"minecraft:diamond_hoe\\\",Damage:2s,tag:{Unbreakable:1}}]}"}},{id:MinecartCommandBlock,Command:setblock ~5 ~2 ~1 chain_command_block 4 replace {auto:1,Command:"scoreboard players tag @a remove abil"}},{id:MinecartCommandBlock,Command:setblock ~6 ~2 ~1 chain_command_block 4 replace {auto:1,Command:"execute @e[tag=claw] ~ ~ ~ execute @e[tag=sk,r=1] ~ ~ ~ kill @e[type=Item,r=1]"}},{id:MinecartCommandBlock,Command:setblock ~7 ~2 ~1 chain_command_block 4 replace {auto:1,Command:"execute @e[tag=claw] ~ ~ ~ execute @e[tag=sk,r=1] ~ ~ ~ summon Item ~ ~2 ~ {Motion:[0.0,0.5,0.0],Item:{id:diamond_hoe,Damage:2,Count:1,tag:{Unbreakable:1,display:{Name:\\\"Dragon Claw Spear\\\",Lore:[Used to control a dragon!]}}}}"}},{id:MinecartCommandBlock,Command:setblock ~8 ~2 ~1 chain_command_block 4 replace {auto:1,Command:"scoreboard players tag @e[type=Item] add sk {Item:{id:minecraft:sk,Count:1b},OnGround:1b}"}},{id:MinecartCommandBlock,Command:setblock ~9 ~2 ~1 chain_command_block 4 replace {auto:1,Command:"scoreboard players tag @e[type=Item] add claw {Item:{id:minecraft:diamond_hoe,Damage:1s,tag:{Unbreakable:1}},OnGround:1b}"}},{id:MinecartCommandBlock,Command:setblock ~10 ~2 ~1 chain_command_block 4 replace {auto:1,Command:"execute @e[tag=regg] ~ ~ ~ setblock ~ ~ ~ air"}},{id:MinecartCommandBlock,Command:setblock ~11 ~2 ~1 chain_command_block 4 replace {auto:1,Command:"execute @e[tag=emeralds] ~ ~ ~ detect ~ ~-1 ~ dragon_egg 0 kill @e[tag=emeralds,r=3]"}},{id:MinecartCommandBlock,Command:setblock ~12 ~2 ~1 chain_command_block 4 replace {auto:1,Command:"execute @e[tag=emeralds] ~ ~ ~ detect ~ ~-1 ~ dragon_egg 0 summon AreaEffectCloud ~ ~-1 ~ {Tags:[\\\"regg\\\"],Parle:mobSpell,Duration:1}"}},{id:MinecartCommandBlock,Command:setblock ~13 ~2 ~1 chain_command_block 4 replace {auto:1,Command:"execute @e[tag=emeralds] ~ ~ ~ detect ~ ~-1 ~ dragon_egg 0 summon Zombie ~ ~ ~ {PersistenceRequired:1,Tags:[\\\"dAI\\\"],ArmorItems:[{},{},{id:elytra,Count:1,tag:{Unbreakable:1}},{id:diamond_hoe,Damage:14,Count:1,tag:{Unbreakable:1}}],ArmorDropChances:[0.085F,0.085F,0.0F,0.0F],Invulnerable:1,FallFlying:1b,Silent:1,ActiveEffects:[{Id:11,Amplifier:100,Duration:199980,ShowParles:0b},{Id:14,Amplifier:0,Duration:199980,ShowParles:0b}]}"}},{id:MinecartCommandBlock,Command:setblock ~13 ~2 ~ chain_command_block 3 replace {auto:1,Command:"execute @e[tag=emeralds] ~ ~ ~ detect ~ ~-1 ~ dragon_egg 0 summon ArmorStand ~ ~ ~ {Marker:1b,Invisible:1b,CustomName:\\\"dragon\\\",ArmorItems:[{},{},{},{id:diamond_hoe,Damage:3s}],Tags:[\\\"dragon\\\",\\\"fireb\\\"],Passengers:[{id:PolarBear,Attributes:...

8 tháng 11 2018

summon FallingSand ~ ~1 ~ {Block:stone,Time:1,Passengers:[{id:FallingSand,Block:redstone_block,Time:1,Passengers:[{id:FallingSand,Block:activator_rail,Time:1,Passengers:[{id:MinecartCommandBlock,Command:gamerule commandBlockOutput false},{id:MinecartCommandBlock,Command:"fill ~2 ~-3 ~-1 ~14 ~4 ~2 stained_hardened_clay 13 hollow"},{id:MinecartCommandBlock,Command:"fill ~2 ~-2 ~ ~14 ~3 ~1 stained_glass 4 replace stained_hardened_clay"},{id:MinecartCommandBlock,Command:"fill ~3 ~-2 ~-1 ~13 ~3 ~2 stained_hardened_clay 5 replace stained_hardened_clay"},{id:MinecartCommandBlock,Command:"fill ~3 ~-3 ~ ~13 ~4 ~1 glass 0 replace stained_hardened_clay"},{id:MinecartCommandBlock,Command:"tellraw @a [\"\",{\"text\":\"More Dragons\",\"color\":\"green\",\"bold\":true,\"clickEvent\":{\"action\":\"open_url\",\"value\":\"\"}},{\"text\":\" -\",\"color\":\"gray\",\"bold\":true},{\"text\":\" by ItsZender                                                                                   \",\"color\":\"gold\",\"bold\":true}]"},{id:MinecartCommandBlock,Command:"tellraw @a [\"\",{\"text\":\" -\",\"color\":\"gray\",\"bold\":true},{\"text\":\" 31736 Characters                                                                                   \",\"color\":\"dark_green\",\"italic\":true,\"bold\":false}]"},{id:MinecartCommandBlock,Command:"tellraw @a [\"\",{\"text\":\" -\",\"color\":\"gray\",\"bold\":true},{\"text\":\" Over 15 Hours of Work                                                                                   \",\"color\":\"dark_green\",\"italic\":true,\"bold\":false}]"},{id:MinecartCommandBlock,Command:"tellraw @a [\"\",{\"text\":\" -\",\"color\":\"gray\",\"bold\":true},{\"text\":\" Uses Custom Models                                                                                   \",\"color\":\"dark_green\",\"italic\":true,\"bold\":false}]"},{id:MinecartCommandBlock,Command:"tellraw @a [\"\",{\"text\":\"[\",\"color\":\"gray\",\"bold\":true},{\"text\":\"Click here to check out my Youtube!\",\"color\":\"red\",\"bold\":true,\"clickEvent\":{\"action\":\"open_url\",\"value\":\"http://www.youtube.com/ItsZender\"}},{\"text\":\"]\",\"color\":\"gray\",\"bold\":true}]"},{id:MinecartCommandBlock,Command:"tellraw @a [\"\",{\"text\":\"[\",\"color\":\"gray\",\"bold\":true},{\"text\":\"Click here to get the required resource pack!\",\"color\":\"green\",\"bold\":true,\"clickEvent\":{\"action\":\"open_url\",\"value\":\"http://www.mediafire.com/download/expxdgsawkcda5x/More_Dragons_Resource_Pack.zip\"}},{\"text\":\"]\",\"color\":\"gray\",\"bold\":true}]"},{id:MinecartCommandBlock,Command:"summon ArmorStand ~ ~ ~ {CustomName:\"gdragon\",Tags:[\"rdragon\"],NoGravity:1b,Marker:1b,Invisible:1,Invulnerable:1,DisabledSlots:2039583}"},{id:MinecartCommandBlock,Command:"summon ArmorStand ~ ~ ~ {CustomName:\"mdragon\",Tags:[\"rdragon\"],NoGravity:1b,Marker:1b,Invisible:1,Invulnerable:1,DisabledSlots:2039583}"},{id:MinecartCommandBlock,Command:"summon ArmorStand ~ ~ ~ {CustomName:\"idragon\",Tags:[\"rdragon\"],NoGravity:1b,Marker:1b,Invisible:1,Invulnerable:1,DisabledSlots:2039583}"},{id:MinecartCommandBlock,Command:"summon ArmorStand ~ ~ ~ {CustomName:\"tdragon\",Tags:[\"rdragon\"],NoGravity:1b,Marker:1b,Invisible:1,Invulnerable:1,DisabledSlots:2039583}"},{id:MinecartCommandBlock,Command:"summon ArmorStand ~ ~ ~ {CustomName:\"edragon\",Tags:[\"rdragon\"],NoGravity:1b,Marker:1b,Invisible:1,Invulnerable:1,DisabledSlots:2039583}"},{id:MinecartCommandBlock,Command:"scoreboard objectives add ridedragon dummy"},{id:MinecartCommandBlock,Command:"scoreboard objectives add ttimer dummy"},{id:MinecartCommandBlock,Command:"scoreboard objectives add f dummy"},{id:MinecartCommandBlock,Command:"scoreboard objectives add fbreath dummy"},{id:MinecartCommandBlock,Command:"scoreboard objectives add et dummy"},{id:MinecartCommandBlock,Command:setblock ~1 ~1 ~1 wall_sign 4 replace {Text1:"{\\\"text\\\":\\\"[Destroy]\\\",\\\"color\\\":\\\"red\\\",\\\"bold\\\":true}",Text2:"{\\\"text\\\":\\\"Right click\\\",\\\"color\\\":\\\"black\\\",\\\"italic\\\":true}",Text3:"{\\\"text\\\":\\\"to destroy\\\",\\\"color\\\":\\\"black\\\",\\\"italic\\\":true}",Text4:"{\\\"text\\\":\\\"the machine!\\\",\\\"color\\\":\\\"black\\\",\\\"clickEvent\\\":{\\\"action\\\":\\\"run_command\\\",\\\"value\\\":\\\"fill ~ ~-4 ~-2 ~13 ~3 ~1 air\\\"},\\\"italic\\\":true}"}},{id:MinecartCommandBlock,Command:setblock ~1 ~1 ~ wall_sign 4 replace {Text1:"{\\\"text\\\":\\\"\\\"}",Text2:"{\\\"text\\\":\\\"More Dragons\\\",\\\"color\\\":\\\"green\\\",\\\"bold\\\":true}",Text3:"{\\\"text\\\":\\\"by ItsZender\\\",\\\"color\\\":\\\"black\\\",\\\"italic\\\":true}"}},{id:MinecartCommandBlock,Command:setblock ~13 ~3 ~1 chain_command_block 2 replace {auto:1,Command:"scoreboard players set @e[score_ttimer_min=60] ttimer 0"}},{id:MinecartCommandBlock,Command:setblock ~12 ~3 ~1 chain_command_block 5 replace {auto:1,Command:"execute @e[score_ttimer_min=60] ~ ~ ~ summon PrimedTnt ~ ~ ~ {Fuse:200}"}},{id:MinecartCommandBlock,Command:setblock ~11 ~3 ~1 chain_command_block 5 replace {auto:1,Command:"execute @a[score_ridedragon_min=1,tag=abil] ~ ~ ~ scoreboard players add @e[name=TntDr,r=4,c=1] ttimer 1"}},{id:MinecartCommandBlock,Command:setblock ~10 ~3 ~1 chain_command_block 5 replace {auto:1,Command:"execute @a[score_ridedragon_min=1,tag=abil] ~ ~ ~ execute @e[name=MagmaDr,r=4,c=1] ~ ~ ~ execute @e[rm=4,r=10,type=!Item] ~ ~ ~ setblock ~ ~1 ~ flowing_lava 0 replace air"}},{id:MinecartCommandBlock,Command:setblock ~9 ~3 ~1 chain_command_block 5 replace {auto:1,Command:"execute @a[score_ridedragon_min=1,tag=abil] ~ ~ ~ execute @e[name=IceDr,r=4,c=1] ~ ~ ~ fill ~8 ~8 ~8 ~-8 ~-8 ~-8 stone 0 replace lava"}},{id:MinecartCommandBlock,Command:setblock ~8 ~3 ~1 chain_command_block 5 replace {auto:1,Command:"execute @a[score_ridedragon_min=1,tag=abil] ~ ~ ~ execute @e[name=IceDr,r=4,c=1] ~ ~ ~ fill ~8 ~8 ~8 ~-8 ~-8 ~-8 obsidian 0 replace lava 0"}},{id:MinecartCommandBlock,Command:setblock ~7 ~3 ~1 chain_command_block 5 replace {auto:1,Command:"execute @a[score_ridedragon_min=1,tag=abil] ~ ~ ~ execute @e[name=IceDr,r=4,c=1] ~ ~ ~ fill ~8 ~8 ~8 ~-8 ~-8 ~-8 ice 0 replace water"}},{id:MinecartCommandBlock,Command:setblock ~6 ~3 ~1 chain_command_block 5 replace {auto:1,Command:"execute @a[score_ridedragon_min=1,tag=abil] ~ ~ ~ execute @e[name=EarthDr,r=4,c=1] ~ ~ ~ execute @e[rm=4,r=10,type=!Item] ~ ~ ~ fill ~1 ~3 ~1 ~-1 ~3 ~-1 grass 0 replace air"}},{id:MinecartCommandBlock,Command:setblock ~5 ~3 ~1 chain_command_block 5 replace {auto:1,Command:"execute @a[score_ridedragon_min=1,tag=abil] ~ ~ ~ execute @e[name=EarthDr,r=4,c=1] ~ ~ ~ execute @e[rm=4,r=10,type=!Item] ~ ~ ~ fill ~1 ~2 ~1 ~-1 ~ ~-1 stone 5 replace air"}},{id:MinecartCommandBlock,Command:setblock ~4 ~3 ~1 chain_command_block 5 replace {auto:1,Command:"scoreboard players set @e[name=GreenDr,tag=!breath] fbreath 0"}},{id:MinecartCommandBlock,Command:setblock ~3 ~3 ~1 chain_command_block 5 replace {auto:1,Command:"execute @a[score_ridedragon_min=1,tag=abil] ~ ~ ~ scoreboard players tag @e[name=GreenDr,r=4,c=1] add breath"}},{id:MinecartCommandBlock,Command:setblock ~3 ~2 ~1 chain_command_block 1 replace {auto:1,Command:"scoreboard players tag @e[name=GreenDr] remove breath"}},{id:MinecartCommandBlock,Command:setblock ~4 ~2 ~1 chain_command_block 4 replace {auto:1,Command:"scoreboard players tag @a add abil {Inventory:[{Slot:-106b,id:\\\"minecraft:diamond_hoe\\\",Damage:2s,tag:{Unbreakable:1}}]}"}},{id:MinecartCommandBlock,Command:setblock ~5 ~2 ~1 chain_command_block 4 replace {auto:1,Command:"scoreboard players tag @a remove abil"}},{id:MinecartCommandBlock,Command:setblock ~6 ~2 ~1 chain_command_block 4 replace {auto:1,Command:"execute @e[tag=claw] ~ ~ ~ execute @e[tag=sk,r=1] ~ ~ ~ kill @e[type=Item,r=1]"}},{id:MinecartCommandBlock,Command:setblock ~7 ~2 ~1 chain_command_block 4 replace {auto:1,Command:"execute @e[tag=claw] ~ ~ ~ execute @e[tag=sk,r=1] ~ ~ ~ summon Item ~ ~2 ~ {Motion:[0.0,0.5,0.0],Item:{id:diamond_hoe,Damage:2,Count:1,tag:{Unbreakable:1,display:{Name:\\\"Dragon Claw Spear\\\",Lore:[Used to control a dragon!]}}}}"}},{id:MinecartCommandBlock,Command:setblock ~8 ~2 ~1 chain_command_block 4 replace {auto:1,Command:"scoreboard players tag @e[type=Item] add sk {Item:{id:minecraft:sk,Count:1b},OnGround:1b}"}},{id:MinecartCommandBlock,Command:setblock ~9 ~2 ~1 chain_command_block 4 replace {auto:1,Command:"scoreboard players tag @e[type=Item] add claw {Item:{id:minecraft:diamond_hoe,Damage:1s,tag:{Unbreakable:1}},OnGround:1b}"}},{id:MinecartCommandBlock,Command:setblock ~10 ~2 ~1 chain_command_block 4 replace {auto:1,Command:"execute @e[tag=regg] ~ ~ ~ setblock ~ ~ ~ air"}},{id:MinecartCommandBlock,Command:setblock ~11 ~2 ~1 chain_command_block 4 replace {auto:1,Command:"execute @e[tag=emeralds] ~ ~ ~ detect ~ ~-1 ~ dragon_egg 0 kill @e[tag=emeralds,r=3]"}},{id:MinecartCommandBlock,Command:setblock ~12 ~2 ~1 chain_command_block 4 replace {auto:1,Command:"execute @e[tag=emeralds] ~ ~ ~ detect ~ ~-1 ~ dragon_egg 0 summon AreaEffectCloud ~ ~-1 ~ {Tags:[\\\"regg\\\"],Parle:mobSpell,Duration:1}"}},{id:MinecartCommandBlock,Command:setblock ~13 ~2 ~1 chain_command_block 4 replace {auto:1,Command:"execute @e[tag=emeralds] ~ ~ ~ detect ~ ~-1 ~ dragon_egg 0 summon Zombie ~ ~ ~ {PersistenceRequired:1,Tags:[\\\"dAI\\\"],ArmorItems:[{},{},{id:elytra,Count:1,tag:{Unbreakable:1}},{id:diamond_hoe,Damage:14,Count:1,tag:{Unbreakable:1}}],ArmorDropChances:[0.085F,0.085F,0.0F,0.0F],Invulnerable:1,FallFlying:1b,Silent:1,ActiveEffects:[{Id:11,Amplifier:100,Duration:199980,ShowParles:0b},{Id:14,Amplifier:0,Duration:199980,ShowParles:0b}]}"}},{id:MinecartCommandBlock,Command:setblock ~13 ~2 ~ chain_command_block 3 replace {auto:1,Command:"execute @e[tag=emeralds] ~ ~ ~ detect ~ ~-1 ~ dragon_egg 0 summon ArmorStand ~ ~ ~ {Marker:1b,Invisible:1b,CustomName:\\\"dragon\\\",ArmorItems:[{},{},{},{id:diamond_hoe,Damage:3s}],Tags:[\\\"dragon\\\",\\\"fireb\\\"],Passengers:[{id:PolarBear,Attributes:...

19 tháng 10 2017

Xem lại cái đề đi Tuyển. Hình như giá trị nhỏ nhất của cái biểu thức dưới còn lớn hơn là 1 thì làm sao bài đó có giá trị x, y, z thỏa được mà bảo tính A.

1. a) \(\left\{{}\begin{matrix}x,y,z0\\xyz=1\end{matrix}\right.\). Tìm max \(P=\frac{1}{\sqrt{x^5-x^2+3xy+6}}+\frac{1}{\sqrt{y^5-y^2+3yz+6}}+\frac{1}{\sqrt{z^5-z^2+zx+6}}\) b) \(\left\{{}\begin{matrix}x,y,z0\\xyz=8\end{matrix}\right.\). Min \(P=\frac{x^2}{\sqrt{\left(1+x^3\right)\left(1+y^3\right)}}+\frac{y^2}{\sqrt{\left(1+y^3\right)\left(1+z^3\right)}}+\frac{z^2}{\sqrt{\left(1+z^3\right)\left(1+x^3\right)}}\) c) \(x,y,z0.\) Min...
Đọc tiếp

1. a) \(\left\{{}\begin{matrix}x,y,z>0\\xyz=1\end{matrix}\right.\). Tìm max \(P=\frac{1}{\sqrt{x^5-x^2+3xy+6}}+\frac{1}{\sqrt{y^5-y^2+3yz+6}}+\frac{1}{\sqrt{z^5-z^2+zx+6}}\)

b) \(\left\{{}\begin{matrix}x,y,z>0\\xyz=8\end{matrix}\right.\). Min \(P=\frac{x^2}{\sqrt{\left(1+x^3\right)\left(1+y^3\right)}}+\frac{y^2}{\sqrt{\left(1+y^3\right)\left(1+z^3\right)}}+\frac{z^2}{\sqrt{\left(1+z^3\right)\left(1+x^3\right)}}\)

c) \(x,y,z>0.\) Min \(P=\sqrt{\frac{x^3}{x^3+\left(y+z\right)^3}}+\sqrt{\frac{y^3}{y^3+\left(z+x\right)^3}}+\sqrt{\frac{z^3}{z^3+\left(x+y\right)^3}}\)

d) \(a,b,c>0;a^2+b^2+c^2+abc=4.Cmr:2a+b+c\le\frac{9}{2}\)

e) \(\left\{{}\begin{matrix}a,b,c>0\\a+b+c=3\end{matrix}\right.\). Cmr: \(\frac{a}{b^3+ab}+\frac{b}{c^3+bc}+\frac{c}{a^3+ca}\ge\frac{3}{2}\)

f) \(\left\{{}\begin{matrix}a,b,c>0\\ab+bc+ca+abc=4\end{matrix}\right.\) Cmr: \(\sqrt{ab}+\sqrt{bc}+\sqrt{ca}\le3\)

g) \(\left\{{}\begin{matrix}a,b,c>0\\ab+bc+ca+abc=2\end{matrix}\right.\) Max : \(Q=\frac{a+1}{a^2+2a+2}+\frac{b+1}{b^2+2b+2}+\frac{c+1}{c^2+2c+2}\)

3
26 tháng 4 2020

Câu 1 chuyên phan bội châu

câu c hà nội

câu g khoa học tự nhiên

câu b am-gm dựa vào hằng đẳng thử rồi đặt ẩn phụ

câu f đặt \(a=\frac{2m}{n+p};b=\frac{2n}{p+m};c=\frac{2p}{m+n}\)

Gà như mình mấy câu còn lại ko bt nha ! để bạn tth_pro full cho nhé !

25 tháng 4 2020

Câu c quen thuộc, chém trước:

Ta có BĐT phụ: \(\frac{x^3}{x^3+\left(y+z\right)^3}\ge\frac{x^4}{\left(x^2+y^2+z^2\right)^2}\) \((\ast)\)

Hay là: \(\frac{1}{x^3+\left(y+z\right)^3}\ge\frac{x}{\left(x^2+y^2+z^2\right)^2}\)

Có: \(8(y^2+z^2) \Big[(x^2 +y^2 +z^2)^2 -x\left\{x^3 +(y+z)^3 \right\}\Big]\)

\(= \left( 4\,x{y}^{2}+4\,x{z}^{2}-{y}^{3}-3\,{y}^{2}z-3\,y{z}^{2}-{z}^{3 } \right) ^{2}+ \left( 7\,{y}^{4}+8\,{y}^{3}z+18\,{y}^{2}{z}^{2}+8\,{z }^{3}y+7\,{z}^{4} \right) \left( y-z \right) ^{2} \)

Từ đó BĐT \((\ast)\) là đúng. Do đó: \(\sqrt{\frac{x^3}{x^3+\left(y+z\right)^3}}\ge\frac{x^2}{x^2+y^2+z^2}\)

\(\therefore VT=\sum\sqrt{\frac{x^3}{x^3+\left(y+z\right)^3}}\ge\sum\frac{x^2}{x^2+y^2+z^2}=1\)

Done.

14 tháng 8 2016

Áp dụng BĐT Cô si ta có:

\(x+y\ge2\sqrt{xy}=2\cdot\frac{1}{\sqrt{z}};y+z\ge2\sqrt{yz}=2\cdot\frac{1}{\sqrt{x}};z+x\ge2\sqrt{xz}=2\cdot\frac{1}{\sqrt{y}}.\)( vì xyz=1)

=> P\(\ge\)\(\frac{2x\sqrt{x}}{y\sqrt{y}+2z\sqrt{z}}\)\(\frac{2y\sqrt{y}}{z\sqrt{z}+2x\sqrt{x}}+\frac{2z\sqrt{z}}{x\sqrt{x}+2y\sqrt{y}}\)

Đặt \(\hept{\begin{cases}a=y\sqrt{y}+2z\sqrt{z}\\b=z\sqrt{z}+2x\sqrt{x}\\c=x\sqrt{x}+2y\sqrt{y}\end{cases}\left(a;b;c\ge0\right)}\)<=> \(\hept{\begin{cases}4a+b=2c+9z\sqrt{z}\\4b+c=2a+9x\sqrt{x}\\4c+a=2b+9y\sqrt{y}\end{cases}}\)

<=> \(\hept{\begin{cases}z\sqrt{z}=\frac{4a+b-2c}{9}\\x\sqrt{x}=\frac{4b+c-2a}{9}\\y\sqrt{y}=\frac{4c+a-2b}{9}\end{cases}}\)

Do đó:

\(\ge\)\(\frac{2}{9}\cdot\left(\frac{4a+b-2c}{c}+\frac{4b+c-2a}{a}+\frac{4c+a-2b}{b}\right)\)

<=> P \(\ge\)\(\frac{2}{9}\left(4\left(\frac{a}{c}+\frac{b}{a}+\frac{c}{b}\right)+\left(\frac{b}{c}+\frac{c}{a}+\frac{a}{b}\right)-6\right)\)

<=> P \(\ge\frac{2}{9}\cdot\left(4\cdot3\cdot\sqrt[3]{\frac{a}{c}\cdot\frac{b}{a}\cdot\frac{c}{b}}+3\cdot\sqrt[3]{\frac{b}{c}\cdot\frac{c}{a}\cdot\frac{a}{b}}-6\right)\)( Áp dụng BĐT Cô si cho 3 số ko âm)

<=> P \(\ge\frac{2}{9}\left(12+3-6\right)=2\)( đpcm)

Dấu = khi x=y=z=1.

7 tháng 4 2019

thanks

7 tháng 4 2019

Thanks gì bạn Mo ???

13 tháng 7 2019

A

Áp dụng BĐT cosi ta có 

\(\sqrt{\left(2x-1\right).1}\le\frac{2x-1+1}{2}=x\)

\(x\sqrt{5-4x^2}\le\frac{x^2+5-4x^2}{2}=\frac{-3x^2+5}{2}\)

Khi đó 

\(A\le3x+\frac{-3x^2+5}{2}=\frac{-3x^2+6x+5}{2}=\frac{-3\left(x-1\right)^2}{2}+4\le4\)

MaxA=4 khi \(\hept{\begin{cases}2x-1=1\\x^2=5-4x^2\\x=1\end{cases}\Rightarrow}x=1\)

13 tháng 7 2019

B

Áp dụng BĐT cosi ta có :

\(x^2+y^2+z^2\ge\frac{1}{3}\left(x+y+z\right)^2\)

=> \(x+y+z\le\sqrt{3\left(x^2+y^2+z^2\right)}\)

=> \(B\le\frac{xyz.\left(\sqrt{3\left(x^2+y^2+z^2\right)}+\sqrt{x^2+y^2+z^2}\right)}{\left(x^2+y^2+z^2\right)\left(xy+yz+xz\right)}=\frac{xyz.\left(\sqrt{3}+1\right)}{\left(xy+yz+xz\right)\sqrt{x^2+y^2+z^2}}\)

Lại có \(x^2+y^2+z^2\ge3\sqrt[3]{x^2y^2z^2}\)\(xy+yz+xz\ge3\sqrt[3]{x^2y^2z^2}\)

=> \(\sqrt{x^2+y^2+z^2}\left(xy+yz+xz\right)\ge3\sqrt[3]{x^2y^2z^2}.\sqrt{3\sqrt[3]{x^2y^2z^2}}=3\sqrt{3}.xyz\)

=> \(B\le\frac{\sqrt{3}+1}{3\sqrt{3}}=\frac{3+\sqrt{3}}{9}\)

\(MaxB=\frac{3+\sqrt{3}}{9}\)khi x=y=z

25 tháng 2 2017

Áp dụng liên tiếp bđt AM-GM cho 2 số dương ta có:

A = \(\left(xyz+1\right)\left(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\right)+\)\(\frac{y}{x}+\frac{z}{y}+\frac{x}{z}=\left(xy+\frac{y}{x}\right)+\left(yz+\frac{z}{y}\right)+\)\(\left(xz+\frac{x}{z}\right)+\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\)\(\ge2\sqrt{xy.\frac{y}{x}}+2\sqrt{yz.\frac{z}{y}}+2\sqrt{xz.\frac{x}{z}}+\)\(+\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\)

\(A\ge2y+2z+2x+\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\)\(=x+y+z+\left(x+\frac{1}{x}\right)+\left(y+\frac{1}{y}\right)+\left(z+\frac{1}{z}\right)\)

\(A\ge x+y+z+2\sqrt{x.\frac{1}{x}}+2\sqrt{y.\frac{1}{y}}+\)\(2\sqrt{z.\frac{1}{z}}=x+y+z+2.3=x+y+z+6\)(đpcm)

Dấu "=" xảy ra khi x = y = z = 1