Question

plz dear solve this problemplz ​

Answer 1

Consider :

$|x| = y$

Given Quadratic equation,

$|x| ^{2} - 5 |x| + 6 = 0$

It transforms to,

${y}^{2} - 5y + 6 = 0$

Solving the equation :

${y}^{2} - 5y + 6 = 0 \\ \\ {y}^{2} - 2y - 3 y + 6 = 0 \\ \\ y(y - 2) - 3(y - 2) = 0 \\ \\ (y - 3)(y - 2) = 0$

First case :

$y - 3 = 0 \\ \\ y = 3 \\ \\ |x| = 3 \\ \\ x = \pm \: 3$

Second case :

$y - 2 = 0 \\ \\ y = 2 \\ \\ |x| = 2 \\ \\ x = \pm \: 2$

Therefore, The real solutions of the given equation are { - 2, - 3, +2, +3}

Answer 2

Please see the attachment