Question

What are the solutions of the equation x^6-9x^3+8= 0 use u substitution to solve

Answer 1

Answer: x = {1, 2}

Explanation:

x⁶ - 9x³ + 8 = 0

Let u = x³

⇒ (x³)² - 9(x³)¹ + 8(x³)⁰ = 0

⇒ u² - 9u + 8 = 0

⇒ (u - 1)(u - 8) = 0

⇒ u = 1 or u = 8

Replace u with x³

x³ = 1 or x³ = 8

Take the cubed root of each side

x = 1 or x = 2