# How do you solve the equation absx=12-x^2?

Apr 17, 2017

The Soln. Set =$\left\{\pm 3\right\} .$

#### Explanation:

Recall that, |x|=x, if x ge 0; and, |x|=-x, if x lt 0.

We can see from the eqn. that $x = 0$ does not satisfy the given eqn.

Therefore, we will consider only $2$ Cases :

Case 1 : $x > 0.$

In this case, taking, $| x | = x ,$ the eqn. becomes,

$x = 12 - {x}^{2} , \mathmr{and} , {x}^{2} + x - 12 = 0.$

$\therefore \underline{{x}^{2} + 4 x} - \underline{3 x - 12} = 0 , \ldots . \left[4 \times 3 = 12 , 4 - 3 = 1\right]$

$\therefore x \left(x + 4\right) - 3 \left(x + 4\right) = 0.$

$\therefore \left(x + 4\right) \left(x - 3\right) = 0$

$\therefore x = - 4 , \mathmr{and} , x = 3.$ Since, $x > 0 , x = 3.$

Case 2 : $x < 0.$

Here, since, $| x | = - x , \text{ we hvae, } {x}^{2} - x - 12 = 0.$

:. x=4, or, x=-3;" but, "x < 0 rArr x=-3.

These roots satisfy the given eqn.

Hence, The Soln. Set =$\left\{\pm 3\right\} .$

Enjoy Maths.!