\((2x-3)^{2}=(4x)^2-8 =(4x)^{2}-12x+9=(4x)^{2}-8 =(4x)^{2}-12x+9-(4x)^{2}+8=0 =12x+17=0 =12x=-17 =x=\dfrac{-1}{12}\)

`(2x-3)^2 = 4x^2-8`

`<=> 4x^2 - 12x + 9 = 4x^2-8`

`<=> 4x^2 - 12x + 9-4x^2 +8=0`

`<=> -12x + 17=0`

`<=>-12x=-17`

`<=> x= 17/12`

vậy phương trình có nghiệm \(S=\left\{\dfrac{17}{12}\right\}\)

\(\left(2x-3\right)^2=4x^2-8\)

\(\Leftrightarrow4x^2-12x+9=4x^2-8\)

\(\Leftrightarrow4x^2-12x+9-4x^2+8=0\)

\(\Leftrightarrow17-12x=0\)

\(\Leftrightarrow12x=17\)

\(\Leftrightarrow x=\dfrac{17}{12}\)

\(\text{Vậy phương trình có tập nghiệm là }S=\left\{\dfrac{17}{12}\right\}\)

2:

a: =>2x^2-4x-2=x^2-x-2

=>x^2-3x=0

=>x=0(loại) hoặc x=3

b: =>(x+1)(x+4)<0

=>-4<x<-1

d: =>x^2-2x-7=-x^2+6x-4

=>2x^2-8x-3=0

=>\(x=\dfrac{4\pm\sqrt{22}}{2}\)

a: =>x=-23

b: (x+2)/(x-2)-1/x=2/x(x-2)

=>x^2+2x-x+2=2

=>x^2+x=0

=>x=0(loại) hoặc x=-1(nhận)

1)3(x^3+1) + 2x(x+1)=8

suy ra : 3(x+1)(x^2 +x+1) + 2x(x+1) =8

suy ra : (x+1) ( 3( x^2+x+1)  +2x) -8 =0

suy ra : (x+1) ( 3x^2 +3x+3+2x) -8 =0

mk ko bt nữa

\(a,2x\left(x-5\right)+4\left(x-5\right)=0\\ \Leftrightarrow\left(x-5\right)\left(2x+4\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x-5=0\\2x+4=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=5\\2x=-4\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=5\\x=-2\end{matrix}\right.\)

Vậy \(x\in\left\{5;-2\right\}\)

\(b,3x-15=2x\left(x-5\right)\\ \Leftrightarrow3\left(x-5\right)-2x\left(x-5\right)=0\\ \Leftrightarrow\left(x-5\right)\left(-2x+3\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x-5=0\\-2x+3=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=5\\2x=3\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=5\\x=\dfrac{3}{2}\end{matrix}\right.\)

Vậy \(x\in\left\{5;\dfrac{3}{2}\right\}\)

\(c,\left(2x+1\right)\left(3x-2\right)=\left(5x-8\right)\left(2x+1\right)\\ \Leftrightarrow\left(2x+1\right)\left(3x-2\right)-\left(5x-8\right)\left(2x+1\right)=0\\ \Leftrightarrow\left(2x+1\right)\left(3x-2-5x+8\right)=0\\ \Leftrightarrow\left(2x+1\right)\left(-2x+6\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}2x+1=0\\-2x+6=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}2x=-1\\2x=6\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{1}{2}\\x=3\end{matrix}\right.\)

Vậy \(x\in\left\{-\dfrac{1}{2};3\right\}\)

Câu d xem lại đề

a: \(\Leftrightarrow\left(-x+3\right)\left(x+6\right)=18\)

\(\Leftrightarrow-x^2-6x+3x+18-18=0\)

\(\Leftrightarrow-x\left(x+3\right)=0\)

=>x=0 hoặc x=-3

b: \(\Leftrightarrow x\left(3x^2+6x-4\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\3x^2+6x-4=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x^2+2x-\dfrac{4}{3}=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\\left(x+1\right)^2=\dfrac{7}{3}\end{matrix}\right.\Leftrightarrow x\in\left\{0;\dfrac{\sqrt{21}}{3}-1;\dfrac{-\sqrt{21}}{3}-1\right\}\)

c: =>x(3x-5)=0

=>x=0 hoặc x=5/3

d: =>(x-2)(x+2)=0

=>x=2 hoặc x=-2