Question

Find one value of x that is a solution to the

X
equation:
(x² − 8)² + x² − 8 = 20
X =

Answer 1

Answer: x = {+-sqrt(3), +-2*sqrt(3)}.

Explanation:

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

▪︎ Let (x^2 - 8) be y.

Then,

y^2 + y = 20

y^2 + y - 20 = 0

D = b^2 - 4ac = 1 + 20*4 = 81 = 9^2

y1 = (-b - sqrt(D))/(2a) = (-1 - 9)/2 = -10/2 = -5

y2 = (-b + sqrt(D))/(2a) = (-1 + 9)/2 = 8/2 = 4

1) x^2 - 8 = -5

x^2 = 8 - 5

x^2 = 3

x = +-sqrt(3)

2) x^2 - 8 = 4

x^2 = 8 + 4

x^2 = 12

x = +-sqrt(12)

x = +-2*sqrt(3)