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  4. The equation |x-x2-1|=|2 x-3-x2| has

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

Complex Numbers and Quadratic Equations

Solution:

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