Does the absolute sign make a difference?

Algebra Level 3

True or False?

$\quad$ Both the equations $x^2 - 5|x|+6 = 0$ and $x^2-5x+6 = 0$ share the same solution.

Notation : $| \cdot |$ denotes the absolute value function .

False True

1 solution

Akshat Sharda
Jul 18, 2016

$x^2-5x+6=0\Rightarrow x=2,3 \\ x^2-5|x|+6=0\Rightarrow |x|=2,3 \Rightarrow x=±2,±3 \\ \text{Note: }x^2=|x|^2$