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

Question

Chen

Mathematics

24 March, 20:05

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

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Answers (1)

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Casey Barnes · Answer 1

Answer: x = {1, 2}

Step-by-step 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