First slide

Theory of expressions

Question

The equation $|x - x^{2} - 1| = |2 x - 3 - x^{2}|$ has

Moderate

A

no solution
B

exactly one solution
C

exactly two solutions
D

more than two solutions

Solution

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

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App