Question

The equation $\left|x-x^2-1\right|=\left|2x-3-x^2\right|$ has

• A. no solution
• B. exactly one solution
• C. exactly two solutions
• D. more than two solutions

Answer 1

Answer: (B)

$\left|x-x^2-1\right|=\left|2x-3-x^2\right|\Rightarrow \left|x^2-x+1\right|=$
\left|x^2-2 x+3\right| $<br/>$\Rightarrow\left|\left(x-\frac{1}{2}\right)^2+\frac{3}{4}\right|=\left|(x-1)^2+2\right|$<br/>$\Rightarrow x^2-x+1=x^2-2 x+3 \Rightarrow x=2$