Question

Helpp ..... i will send the options for the answers

Answer 1

2, -2, and 0.

Step-by-step explanation:

First, we need to factorize the left side of the equation as:

(x² + 4)² + 32 = 12x² + 48

(x² + 4)² + 32 = 12( x² + 4)

Now, we need to substitute a = x² + 4, so:

a² + 32 = 12a

So, solving for a, we get:

a² + 32 - 12a = 12a - 12a

a² + 32 - 12a = 0

a² - 12a + 32 = 0

(a - 8)(a - 4) = 0

Then:

a - 8 = 0

a - 8 + 8 = 0 + 8

a = 8

or

a - 4 = 0

a - 4 + 4 = 0 + 4

a = 4

Then, a is equal to x² + 4, so replacing a by x² + 4 on each solution for a, we get:

For a = 8:

x² + 4 = 8

x² + 4 - 4 = 8 - 4

x² = 4

x = ±√4

x = ± 2

For a = 4:

x² + 4 = 4

x² + 4 - 4 = 4 - 4

x² = 0

x = 0

Therefore, the solutions for x are 2, -2, and 0.