Question

Let a= x^2 +4. Rewrite the following equation in terms of a and set it equal to zero.

(x^2+4)^2+32=12x^2+48

which of the following are solutions for x?

A)-8
B)-2
C)4
D)0
E)2
F)-4
G)8

Answer 1

C and G

Explanation:

(x^2+4)^2+32=12x^2+48 is written as
`(x^2+4)^2+32=12x^2+48`.

We can simplify the expression using the term a by replacing x^2 + 4 with a.

`(x^2+4)^2+32=12x^2+48\\(x^2+4)^2+32=12(x^2+4)\\a^2 + 32 = 12a\\a^2 - 12a + 32 = 0`

This factors into (a-4)(a-8). Solve by setting each factor equal to 0 and solve for a.

a-4 = 0 a=4

a-8=0 a=8