6*4*57+12*29*2+3*14*8
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\(\left(19\frac{5}{8}:\frac{7}{12}-13\frac{1}{4}:\frac{7}{12}\right).\frac{4}{5}\)
\(=\left(\frac{157}{8}:\frac{7}{12}-\frac{53}{4}:\frac{7}{12}\right).\frac{4}{5}\)
\(=\left[\left(\frac{157}{8}-\frac{53}{4}\right):\frac{7}{12}\right].\frac{4}{5}\)
\(=\left[\frac{51}{8}:\frac{7}{12}\right].\frac{4}{5}\)
\(=\frac{153}{14}.\frac{4}{5}\)
\(=\frac{306}{35}\)
\(\left(\frac{-2}{5}+\frac{3}{7}\right)-\left(\frac{4}{9}+\frac{12}{20}-\frac{13}{35}\right)+\frac{7}{35}\)
\(=\frac{1}{35}-\frac{212}{315}+\frac{7}{35}\)
\(=\frac{1}{35}+\frac{-212}{315}+\frac{7}{35}\)
\(=\frac{9}{315}+\frac{-212}{315}+\frac{63}{315}\)
\(=\frac{-140}{315}=\frac{-4}{9}\)
a: ta có: \(7-\left(2x-\frac13\right)^2=3\)
=>\(\left(2x-\frac13\right)^2=7-3=4\)
=>\(\left[\begin{array}{l}2x-\frac13=2\\ 2x-\frac13=-2\end{array}\right.\Rightarrow\left[\begin{array}{l}2x=2+\frac13=\frac73\\ 2x=-2+\frac13=-\frac53\end{array}\right.\)
=>\(\left[\begin{array}{l}x=\frac73:2=\frac76\\ x=-\frac53:2=-\frac56\end{array}\right.\)
b: \(\left(2x+\frac13\right)^2-\frac38=\frac18\)
=>\(\left(2x+\frac13\right)^2=\frac38+\frac18=\frac48=\frac12\)
=>\(2x+\frac13=\sqrt{\frac12}=\frac{\sqrt2}{2}\)
=>\(2x=\frac{\sqrt2}{2}-\frac13=\frac{3\sqrt2-2}{6}\)
=>\(x=\frac{3\sqrt2-2}{12}\)
c: \(12:\left\lbrack29-\left(x-\frac23\right)^2\right\rbrack=3\)
=>\(29-\left(x-\frac23\right)^2=12:3=4\)
=>\(\left(x-\frac23\right)^2=29-4=25\)
=>\(\left[\begin{array}{l}x-\frac23=5\\ x-\frac23=-5\end{array}\right.\Rightarrow\left[\begin{array}{l}x=5+\frac23=\frac{17}{3}\\ x=-5+\frac23=-\frac{13}{3}\end{array}\right.\)
d: \(\left(3x-\frac12\right)^3+\frac83=\frac{29}{9}-\frac{14}{27}\)
=>\(\left(3x-\frac12\right)^3+\frac83=\frac{87}{27}-\frac{14}{27}=\frac{73}{27}\)
=>\(\left(3x-\frac12\right)^3=\frac{73}{27}-\frac83=\frac{73}{27}-\frac{72}{27}=\frac{1}{27}=\left(\frac13\right)^3\)
=>\(3x-\frac12=\frac13\)
=>\(3x=\frac12+\frac13=\frac56\)
=>\(x=\frac{5}{18}\)
e: \(2\left(2x-\frac13\right)^2+\frac43=\frac56+\frac{13}{18}\)
=>\(2\left(2x-\frac13\right)^2=\frac{15}{18}+\frac{13}{18}-\frac43=\frac{28}{18}-\frac{24}{18}=\frac{4}{18}=\frac29\)
=>\(\left(2x-\frac13\right)^2=\frac19\)
=>\(\left[\begin{array}{l}2x-\frac13=\frac13\\ 2x-\frac13=-\frac13\end{array}\right.\Rightarrow\left[\begin{array}{l}2x=\frac23\\ 2x=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=\frac13\\ x=0\end{array}\right.\)
2 . 53 . 27 + 6 . 9 . 87 - 3 . 18 . 40
= 2. 53 . 9 . 3 + 2. 3 .9 .87 - 3 .2 .9 .40
= 54.53+54.87-54.40
=54(53+87-40)
=54. 100=5400
12 . 25 + 29 . 25 + 59 . 25
= 25 . ( 12+29+59)
=25 . 90
=2250
43 . 37 + 93 . 43 + 57 . 61 + 69 . 57
= 43.(37+93)+57(61+69)
=43.130+57.130
=130.(43+57)
=130.100
=13 000
12 . 53 + 53 . 172 - 53
=53(12+172-1)
=53.184
=9752
35 . 54 + 35 . 58 + 65 . 75 + 65 . 45
=35(54+58)+65(75+45)
=35.112+65.120
=3920+7800
=11720
39 . 8 + 70 . 3 + 31 . 8
=8(39+31)+70.3
=8.70+70.3
=70.(8+3)
=70.11
=770