Đáp án:
`S=\{-5/2;1/2\}`
Giải thích các bước giải:
`(2x+1)(x+1)^2(2x+3)=18`
`⇔4(x+1)^2(2x+1)(2x+3)=72`
`⇔[2(x+1)]^2(2x+1)(2x+3)=72`
`⇔(2x+2)^2(2x+1)(2x+3)=72`
`⇔(4x^2+8x+4)(4x^2+8x+3)=72`
Đặt `4x^2+8x+4=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`
`⇒4x^2+8x+4=9`
`⇔4x^2+8x-5=0`
`⇔4x^2+10x-2x-5=0`
`⇔2x(2x+5)-(2x+5)=0`
`⇔(2x+5)(2x-1)=0`
\(⇔\left[ \begin{array}{l}2x+5=0\\2x-1=0\end{array} \right.\)
\(⇔\left[ \begin{array}{l}x=\dfrac{-5}{2}\\x=\dfrac{1}{2}\end{array} \right.\)
Vậy `S=\{-5/2;1/2\}`
