`(2x-5)^2=9/16`
`(2x-5)^2=`\(\left(\pm\dfrac{3}{4}\right)^2\)
`=>` \(\left[{}\begin{matrix}2x-5=\dfrac{3}{4}\\2x-5=-\dfrac{3}{4}\end{matrix}\right.\)
`=>` \(\left[{}\begin{matrix}2x=\dfrac{3}{4}+5\\2x=-\dfrac{3}{4}+5\end{matrix}\right.\)
`=>` \(\left[{}\begin{matrix}2x=\dfrac{3}{4}+\dfrac{20}{5}\\2x=-\dfrac{3}{4}+\dfrac{20}{5}\end{matrix}\right.\)
`=>` \(\left[{}\begin{matrix}2x=\dfrac{23}{5}\\2x=\dfrac{17}{5}\end{matrix}\right.\)
`=>` \(\left[{}\begin{matrix}x=\dfrac{23}{5}:2\\x=\dfrac{17}{5}:2\end{matrix}\right.\)
`=>` \(\left[{}\begin{matrix}x=\dfrac{23}{5}.\dfrac{1}{2}\\x=\dfrac{17}{5}.\dfrac{1}{2}\end{matrix}\right.\)
`=>` \(\left[{}\begin{matrix}x=\dfrac{23}{10}\\x=\dfrac{17}{10}\end{matrix}\right.\)
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`(1-2x)^3 = -27/64`
`(1-2x)^3 = (-3/4)^3`
`1-2x=-3/4`
`2x=1-(-3/4)`
`2x=1+3/4`
`2x=7/4`
`x=7/4 : 2`
`x=7/4 xx 1/2`
`x=7/8`
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`(3x+1/2)^4 = 0`
`(3x+1/2)^4 = 0^4`
`3x+1/2 = 0`
`3x=0-1/2`
`3x=-1/2`
`x=-1/2 : 3`
`x=-1/2 xx 1/3`
`x=-1/6`
____________________________
`(x+3/4)^3 + 5 = -3`
`(x+3/4)^3 =-3-5`
`(x+3/4)^3 = -8`
`(x+3/4)^3=(-2)^3`
`x+3/4=-2`
`x=-2 + 3/4`
`x=-4/4 + 3/4`
`x=-1/4`
________________________
`(x-1/5)^2 = 1/4`
`(x-1/5)^2 =`\(\left(\pm\dfrac{1}{2}\right)^2\)
`@TH1:`
`x-1/5=1/2`
`x=1/2+1/5`
`x=5/10+2/10`
`x=7/10`
`@TH2:`
`x-1/5=-1/2`
`x=-1/2 + 1/5`
`x=-5/10 + 2/10`
`x=-3/10`
Vậy `x = {-3/10; 7/10}`
\(1,\left(2x-5\right)^2=\dfrac{9}{16}\)
\(\Leftrightarrow\left|2x-5\right|=\dfrac{3}{4}\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-5=\dfrac{3}{4}\\2x-5=-\dfrac{3}{4}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{23}{8}\\x=\dfrac{17}{8}\end{matrix}\right.\)
\(2,\left(1-2x\right)^3=-\dfrac{27}{64}\)
\(\Leftrightarrow1-2x=-\dfrac{3}{4}\)
\(\Leftrightarrow x=\dfrac{7}{8}\)
\(3,\left(3x+\dfrac{1}{2}\right)^4=0\)
\(\Leftrightarrow3x+\dfrac{1}{2}=0\)
\(\Leftrightarrow x=-\dfrac{1}{6}\)
\(4,\left(x+\dfrac{3}{4}\right)^3+5=-3\)
\(\Leftrightarrow\left(x+\dfrac{3}{4}\right)^3=-8\)
\(\Leftrightarrow x+\dfrac{3}{4}=-2\)
\(\Leftrightarrow x=-\dfrac{11}{4}\)
\(5,\left(x-\dfrac{1}{5}\right)^2=\dfrac{1}{4}\)
\(\Leftrightarrow\left|x-\dfrac{1}{5}\right|=\dfrac{1}{2}\)
\(\Leftrightarrow\left[{}\begin{matrix}x-\dfrac{1}{5}=\dfrac{1}{2}\\x-\dfrac{1}{5}=-\dfrac{1}{2}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{7}{10}\\x=-\dfrac{3}{10}\end{matrix}\right.\)
\(6,2x=\dfrac{84}{163}\)
\(\Leftrightarrow x=\dfrac{42}{163}\)