Đáp án:
`S=\{1;-1/2\}`
Giải thích các bước giải:
`x(4x-1)^2(2x-1)=9`
`⇔8x(4x-1)^2(2x-1)=9.8`
`⇔(4x-1)^{2}.8x(2x-1)=72`
`⇔(16x^2-8x+1)(16x^2-8x)=72`
Đặt `16x^2-8x+1=a(DK:a>0)`
`⇒` Phương trình trở thành:
`a(a-1)=72`
`⇔a^2+a=72`
`⇔a^2-a-72=0`
`⇔a^2-9a+8a-72=0`
`⇔a(a-9)+8(a-9)=0`
`⇔(a-9)(a+8)=0`
\(⇔\left[ \begin{array}{l}a-9=0\\a+8=0\end{array} \right.\)
\(\left[ \begin{array}{l}a=9(TM)\\a=-8(KTM)\end{array} \right.\)
Với `a=9`
`⇒16x^2-8x+1=9`
`⇔16x^2-8x-8=0`
`⇔8(2x^2-x-1)=0`
`⇔2x^2-x-1=0`
`⇔2x^2-2x+x-1=0`
`⇔2x(x-1)+(x-1)=0`
`⇔(x-1)(2x+1)=0`
\(⇔\left[ \begin{array}{l}x-1=0\\2x+1=0\end{array} \right.\)
\(⇔\left[ \begin{array}{l}x=1\\x=\dfrac{-1}{2}\end{array} \right.\)
Vậy `S=\{1;-1/2\}`
