Question

Solve: |x2 - 4 | = x + 2

Answer 1

Answer:

C.

$x = 1 \: or \: x = - 2 \: or \: x = 3$

Step-by-step explanation:

The give absolute value equation is:

$| {x}^{2} - 4 | = x + 2$ Using the definition of absolute value:

$({x}^{2} - 4) = - (x + 2) \: or \: ({x}^{2} - 4) = + (x + 2)$

This implies that:

${x}^{2} - 4= - x - 2 \: or \: {x}^{2} - 4= x + 2$

Rewrite both equations in standard form:

${x}^{2} + x- 2= 0 \: or \: {x}^{2} - x- 6= 0$

$(x - 1)(x + 2) = 0 \: or \: (x + 2)(x - 3) = 0$

$x = 1 \: or \: x = - 2 \: or \: x = 3$