Question

Find one value of x that is a solution to the equation:(x^2– 8)^2 + x^2 – 8 = 20x=​

Answer 1

Answer:

x = 2 sqrt(3) or x = -2 sqrt(3) or x = sqrt(3) or x = -sqrt(3)

Step-by-step explanation:

Solve for x:

-8 + x^2 + (x^2 - 8)^2 = 20

Expand out terms of the left hand side:

x^4 - 15 x^2 + 56 = 20

Subtract 20 from both sides:

x^4 - 15 x^2 + 36 = 0

Substitute y = x^2:

y^2 - 15 y + 36 = 0

The left hand side factors into a product with two terms:

(y - 12) (y - 3) = 0

Split into two equations:

y - 12 = 0 or y - 3 = 0

Add 12 to both sides:

y = 12 or y - 3 = 0

Substitute back for y = x^2:

x^2 = 12 or y - 3 = 0

Take the square root of both sides:

x = 2 sqrt(3) or x = -2 sqrt(3) or y - 3 = 0

Add 3 to both sides:

x = 2 sqrt(3) or x = -2 sqrt(3) or y = 3

Substitute back for y = x^2:

x = 2 sqrt(3) or x = -2 sqrt(3) or x^2 = 3

Take the square root of both sides:

Answer: x = 2 sqrt(3) or x = -2 sqrt(3) or x = sqrt(3) or x = -sqrt(3)