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35(14-23)-23(14-35)=
=35.14-23-23.14-35
=(35-35).(14-14).(23-23)
= 0 . 0 . 0
= 0
\(-\dfrac{2}{3}=\dfrac{x}{-6}\Rightarrow x=\left(-\dfrac{2}{3}\right)\left(-6\right)=4\)
\(-\dfrac{2}{3}=\dfrac{10}{-y}\Rightarrow y=\left(-10\right):\left(-\dfrac{2}{3}\right)=15\)
\(-\dfrac{2}{3}=\dfrac{z}{9}\Rightarrow z=\left(-\dfrac{2}{3}\right).9=-6\)
\(\dfrac{-2}{3}=\dfrac{x}{-6}=\dfrac{10}{-y}=\dfrac{z}{9}\)
\(x=\left(-6.-2\right):3=4;y=\left(-6.10\right):-4=15;z=\left(10.9\right):-15=-6\)
a: \(\left(\frac{1}{24}-\frac{3}{16}\right):\left(-\frac38+\frac12\right)\)
\(=\left(\frac{2}{48}-\frac{9}{48}\right):\left(-\frac38+\frac48\right)\)
\(=\frac{-7}{48}:\frac18=-\frac{7}{48}\cdot8=-\frac76\)
b: \(-\frac57:\left(5-4\frac47\right)+\left(15\frac13\cdot\frac{-1}{23}\right)\)
\(=-\frac57:\left(5-4-\frac47\right)+\frac{46}{3}\cdot\frac{-1}{23}=-\frac57:\left(1-\frac47\right)+\frac{-2}{3}\)
\(=-\frac57:\frac37+\frac{-2}{3}=-\frac53-\frac23=-\frac73\)
c: \(\left(-2\frac23\cdot1\frac45+2\frac56\right):\left(\frac16-\frac34\right)\)
\(=\left(-\frac83\cdot\frac95+\frac{17}{6}\right):\left(\frac{2}{12}-\frac{9}{12}\right)\)
\(=\left(-\frac{24}{5}+\frac{17}{6}\right):\frac{-7}{12}=\left(-\frac{144}{30}+\frac{85}{30}\right):\frac{-7}{12}\)
\(=-\frac{59}{30}\cdot\frac{12}{-7}=\frac{59\cdot2}{7\cdot5}=\frac{118}{35}\)
d: \(\left(\frac{1}{3^2}-\frac{1}{7^2}\right)\left(\frac{1}{4^2}-\frac{1}{7^2}\right)\cdot\ldots\cdot\left(\frac{1}{49^2}-\frac{1}{7^2}\right)\)
\(=\left(\frac{1}{3^2}-\frac{1}{7^2}\right)\left(\frac{1}{4^2}-\frac{1}{7^2}\right)\cdot\ldots\cdot\left(\frac{1}{7^2}-\frac{1}{7^2}\right)\cdot\left(\frac{1}{8^2}-\frac{1}{7^2}\right)\cdot\ldots\cdot\left(\frac{1}{49^2}-\frac{1}{7^2}\right)\)
\(=\left(\frac{1}{3^2}-\frac{1}{7^2}\right)\left(\frac{1}{4^2}-\frac{1}{7^2}\right)\cdot\ldots\cdot\left(\frac{1}{49}-\frac{1}{49}\right)\cdot\left(\frac{1}{8^2}-\frac{1}{7^2}\right)\cdot\ldots\cdot\left(\frac{1}{49^2}-\frac{1}{7^2}\right)\)
\(=\left(\frac{1}{3^2}-\frac{1}{7^2}\right)\left(\frac{1}{4^2}-\frac{1}{7^2}\right)\cdot\ldots\cdot0\cdot\left(\frac{1}{8^2}-\frac{1}{7^2}\right)\cdot\ldots\cdot\left(\frac{1}{49^2}-\frac{1}{7^2}\right)\)
=0
e: \(\left(1-\frac23\right)\left(1-\frac25\right)\left(1-\frac27\right)\cdot\ldots\cdot\left(1-\frac{2}{2023}\right)\)
\(=\frac13\cdot\frac35\cdot\frac57\cdot\ldots\cdot\frac{2021}{2023}=\frac{1}{2023}\)
f: \(\left(\frac{1}{2^2}-1\right)\left(\frac{1}{3^2}-1\right)\cdot\ldots\cdot\left(\frac{1}{100^2}-1\right)\)
\(=\left(\frac12-1\right)\left(\frac13-1\right)\cdot\ldots\cdot\left(\frac{1}{100}-1\right)\left(\frac12+1\right)\left(\frac13+1\right)\cdot\ldots\cdot\left(\frac{1}{100}+1\right)\)
\(=\frac{-1}{2}\cdot\frac{-2}{3}\cdot\ldots\cdot\frac{-99}{100}\cdot\frac32\cdot\frac43\cdot\ldots\cdot\frac{101}{100}=\frac{-1}{100}\cdot\frac{101}{2}=-\frac{101}{200}\)
g:
Ta có công thức sau:
\(1-\frac{2}{n\left(n+1\right)}\)
\(=\frac{n\left(n+1\right)-2}{n\left(n+1\right)}\)
\(=\frac{n^2+n-2}{n\left(n+1\right)}=\frac{\left(n+2\right)\left(n-1\right)}{n\left(n+1\right)}\)
\(\left(1-\frac13\right)\left(1-\frac16\right)\left(1-\frac{1}{10}\right)\left(1-\frac{1}{15}\right)\cdot\ldots\cdot\left(1-\frac{1}{780}\right)\)
\(=\left(1-\frac26\right)\left(1-\frac{2}{12}\right)\left(1-\frac{2}{20}\right)\left(1-\frac{2}{30}\right)\cdot\ldots\cdot\left(1-\frac{2}{1560}\right)\)
\(=\left(1-\frac{2}{2\cdot3}\right)\left(1-\frac{2}{3\cdot4}\right)\cdot\ldots\cdot\left(1-\frac{2}{39\cdot40}\right)\)
\(=\frac{\left(2+2\right)\left(2-1\right)}{2\left(2+1\right)}\cdot\frac{\left(3+2\right)\left(3-1\right)}{3\left(3+1\right)}\cdot\ldots\cdot\frac{\left(39+2\right)\left(39-1\right)}{39\left(39+1\right)}\)
\(=\frac{4\cdot1}{2\cdot3}\cdot\frac{5\cdot2}{3\cdot4}\cdot\ldots\cdot\frac{41\cdot38}{39\cdot40}=\frac{4\cdot5\cdot\ldots\cdot41}{3\cdot4\cdot..\cdot40}\cdot\frac{1\cdot2\cdot\ldots\cdot38}{2\cdot3\cdot\ldots\cdot39}\)
\(=\frac{41}{3}\cdot\frac{1}{39}=\frac{41}{117}\)
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2 , Mèo máy Doraemon
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4 , Cái bếp lửa
Mình nghĩ thế thôi nhé bạn . Sai thì thôi nhé
Kết bạn nhé
a) 3x+27=9
3x=9-27
3x=(-18)
x=(-6)
Vậy: x=(-6)
c)2.x2-1=49
2.x2=49+1=50
x2=50:2
x2=25=52=(-5)2
\(\Rightarrow\)\(\left[{}\begin{matrix}x=5\\x=\left(-5\right)\end{matrix}\right.\)
Vậy:...........
a) 3x + 27 = 9
=> 3x = - 18
=> x = - 6
b) 2x + 12 = 3(-7)
=> 2x + 12 = - 21
=> 2x = - 33
=> x = -33/2
c) 2x^2 - 1 = 49
=> 2x^2 = 50
=> x^2 = 25
=> x = ±5
số chia:7
thương:23
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