What are the solutions of the equation x⁶ - 9x³ + 8 = 0? Use u substitution to solve.

Solution:

x⁶ - 9x³ + 8 = 0 [Given]

Consider u = x³

So the given equation becomes a quadratic.

u² - 9u + 8 = 0

By splitting the middle term, we solve the quadratic equation.

u² - 1u - 8u + 8 = 0

Taking u as common in the first two terms and 8 as common in the next two terms

u (u - 1) - 8 (u - 1) = 0

(u - 8) (u - 1) = 0

So we get

u - 8 = 0 or u - 1 = 0

u = 8 or u = 1

Substituting the value of u

x³ = 1

x³ = 8

So we get x = 1, 2.

Therefore, the solutions of the equation are x = 1, 2.

---

What are the solutions of the equation x⁶ - 9x³ + 8 = 0? Use u substitution to solve.

Summary:

The solutions of the equation x⁶ - 9x³ + 8 = 0 using u substitution are x = 1, 2.