Solve x4 - 17x2 + 16 = 0. Let u =

this is a question on my test

Solve for x over the real numbers:

x^4 - 17 x^2 + 16 = 0

Substitute y = x^2:

y^2 - 17 y + 16 = 0

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

(y - 16) (y - 1) = 0

Split into two equations:

y - 16 = 0 or y - 1 = 0

Add 16 to both sides:

y = 16 or y - 1 = 0

Substitute back for y = x^2:

x^2 = 16 or y - 1 = 0

Take the square root of both sides:

x = 4 or x = - 4 or y - 1 = 0

Add 1 to both sides:

x = 4 or x = - 4 or y = 1

Substitute back for y = x^2:

x = 4 or x = - 4 or x^2 = 1

Take the square root of both sides:

Answer: x = 4 or x = - 4 or x = 1 or x = - 1