Đáp án:
`1`\(\left[ \begin{array}{l}x=0\\x=1\\x=-2\\x=-3\end{array} \right.\)
`2`\(\left[ \begin{array}{l}x=0\\x=\dfrac{3}{2}\\x=1\\x=\dfrac{-1}{2}\end{array} \right.\)
Giải thích các bước giải:
`1, (x+1)^2-3|x+1|+2=0`
`<=> x^2+2x+1-3|x+1|+2=0`
`<=> x^2+2x+3=3|x+1|`
`<=>`\(\left[ \begin{array}{l}3(x+1)=x^2+2x+3\\3(x+1)=-x^2-2x-3\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x^2-x=0\\x^2+5x+6=0\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x(x-1)=0\\(x+2)(x+3)=0\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=0\\x=1\\x=-2\\x=-3\end{array} \right.\)
`2, 4x(x-1)=|2x-1|+1`
`<=> 4x^2-4x-1=|2x-1|`
`<=>`\(\left[ \begin{array}{l}2x-1=4x^2-4x-1\\2x-1=-4x^2+4x+1\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}4x^2-6x=0\\4x^2-2x-2=0\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}2x(2x-3)=0\\2(x-1)(2x+1)=0\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=0\\x=\dfrac{3}{2}\\x=1\\x=\dfrac{-1}{2}\end{array} \right.\)