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Solve: |x2 - 4 | = x + 2
Select the appropriate response:
A) x=7 x=5
B) x=2 x=3 x=4
C) x=-2 x=3 x=1

Respuesta :

kudzordzifrancis

Answer:

C.

[tex]x = 1 \: or \: x = - 2 \: or \: x = 3[/tex]

Step-by-step explanation:

The give absolute value equation is:

[tex] | {x}^{2} - 4 | = x + 2[/tex] Using the definition of absolute value:

[tex]({x}^{2} - 4) = - (x + 2) \: or \: ({x}^{2} - 4) = + (x + 2)[/tex]

This implies that:

[tex]{x}^{2} - 4= - x - 2 \: or \: {x}^{2} - 4= x + 2[/tex]

Rewrite both equations in standard form:

[tex]{x}^{2} + x- 2= 0 \: or \: {x}^{2} - x- 6= 0[/tex]

[tex](x - 1)(x + 2) = 0 \: or \: (x + 2)(x - 3) = 0[/tex]

[tex]x = 1 \: or \: x = - 2 \: or \: x = 3[/tex]