Question

If $2|x+1{|}^2-3|x+1|+1=0$, then $x=$

• A. $0$
• B. $-2$
• C. $-\frac{1}{2}$
• D. $-\frac{3}{2}$

Answer 1

Answer: (A), (B), (C), (D)

$-\frac{3}{2}$

$2|x+1{|}^2-3|x+1|+1=0\Rightarrow (2|x+1|-1)(|x+1|-1)=0\Rightarrow 2|x+1|-1=0\text{or}|x+1|-1=0\Rightarrow |x+1|=\frac{1}{2}\text{or}|x+1|=1\Rightarrow x=-\frac{1}{2},-\frac{3}{2}\text{or}x=0,-2$