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a) \(4\left(\frac{1}{2}x-\frac{1}{3}\right)^2+5=\frac{61}{9}\)
=> \(4\left(\frac{1}{2}x-\frac{1}{3}\right)^2=\frac{61}{9}-5\)
=> \(4\left(\frac{1}{2}x-\frac{1}{3}\right)^2=\frac{16}{9}\)
=> \(\left(\frac{1}{2}x-\frac{1}{3}\right)^2=\frac{16}{9}:4\)
=> \(\left(\frac{1}{2}x-\frac{1}{3}\right)^2=\frac{16}{9\cdot4}=\frac{16}{36}=\frac{4}{9}\)
=> \(\frac{1}{2}x-\frac{1}{3}=\pm\frac{2}{3}\)
Trường hợp 1 : \(\frac{1}{2}x-\frac{1}{3}=\frac{2}{3}\)
=> \(\frac{1}{2}x=1\)
=> \(x=1:\frac{1}{2}=2\)
Trường hợp 2 : \(\frac{1}{2}x-\frac{1}{3}=-\frac{2}{3}\)
=> \(\frac{1}{2}x=-\frac{2}{3}+\frac{1}{3}=-\frac{1}{3}\)
=> \(x=\left(-\frac{1}{3}\right):\frac{1}{2}=\left(-\frac{1}{3}\right)\cdot2=-\frac{2}{3}\)
b) \(9\left(2x-\frac{1}{3}\right)^3-1=-\frac{2}{3}\)
=> \(9\left(2x-\frac{1}{3}\right)^3=-\frac{2}{3}+1=\frac{1}{3}\)
=> \(\left(2x-\frac{1}{3}\right)^3=\frac{1}{3}:9\)
=> \(\left(2x-\frac{1}{3}\right)^3=\frac{1}{3\cdot9}=\frac{1}{27}\)
=> \(2x-\frac{1}{3}=\frac{1}{3}\)
=> \(2x=\frac{2}{3}\)
=> \(x=\frac{2}{3}:2=\frac{1}{3}\)
Bài cuối tương tự
a) | 5/4x -7/2| - | 5/8x + 3/5| = 0
|5/4x - 7/2| = | 5/8x + 3/5|
TH1: 5/4x - 7/2 = 5/8x + 3/5
=> 5/4x - 5/8x = 3/5 +7/2
5/8x = 41/10
x = 41/10:5/8
x = 164/25
TH2: 5/4x - 7/2 = -5/8x - 3/5
=> 5/4x + 5/8x = -3/5 +7/2
15/8x = 29/10
x = 29/10 : 15/8
x = 116/75
KL: x = 164/25 hoặc x = 116/75
các bài cn lại b lm tương tự nha! h lm dài lắm!
2: 12-10x=25-30x
=>20x=13
=>x=13/20
3: \(3\left(2x+3\right)-2\left(4x-5\right)=10x+21\)
=>6x+9-8x+10=10x+21
=>10x+21=-2x+19
=>12x=-2
=>x=-1/6
4: \(\Leftrightarrow25x-15-6x+12=11-5x\)
=>19x-3=11-5x
=>24x=14
=>x=7/12
5: \(\Leftrightarrow8-12x-5+10x=4-6x\)
=>4-6x=-2x+3
=>-4x=-1
=>x=1/4
6: \(\Leftrightarrow32x-24-6+9x=13-40x\)
=>41x-30=13-40x
=>81x=43
=>x=43/81
7: \(\Leftrightarrow10x-5+20x=5x-11\)
=>30x-5=5x-11
=>25x=-6
=>x=-6/25
a: \(\Leftrightarrow x\cdot\dfrac{1}{2}=\dfrac{1}{4}\cdot\dfrac{-7}{2}+\dfrac{5}{3}=\dfrac{19}{24}\)
hay x=19/12
b: \(\Leftrightarrow\left(\dfrac{45}{11}-3x\right)\cdot\dfrac{11}{5}=\dfrac{21}{5}\)
\(\Leftrightarrow-3x+\dfrac{45}{11}=\dfrac{21}{11}\)
=>-3x=-24/11
=>x=8/11
c: \(\Leftrightarrow\left[{}\begin{matrix}3x-1=0\\5-\dfrac{1}{2}x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{3}\\x=10\end{matrix}\right.\)
d: \(\Leftrightarrow\left(2x+\dfrac{3}{5}\right)^2=\dfrac{16}{25}\)
\(\Leftrightarrow\left[{}\begin{matrix}2x+\dfrac{3}{5}=\dfrac{4}{5}\\2x+\dfrac{3}{5}=-\dfrac{4}{5}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{10}\\x=-\dfrac{7}{10}\end{matrix}\right.\)
\(a,-5.\left(-x+7\right)-3.\left(-x-5\right)=-4.\left(12-x\right)+48\)
\(5x-35-3x+15=-48+4x+48\)
\(2x-10=4x\)
\(2x-4x=10\)
\(-2x=10\)
\(x=-5\)
\(b,\left(-x-7\right)-5.\left(-x-3\right)=12.\left(3-x\right)\)
\(-x-7+5x+15=36-12x\)
\(4x+8=36-12x\)
\(4x+12x=36-8\)
\(16x=28\)
\(x=1,75\)
các câu còn lại tương tự nha