Question

Solve the following equation for x :
1. x^2/3 + x^1/3 – 2 = 0

Answer 1

Answer:

Given equation is x 2/3 + x 1/3 - 2 = 0

Putting x 1/3 = y, the given equation becomes

y2 + y – 2 = 0

⇒ y2 + 2y – y – 2 = 0

⇒ y(y+ 2) – 1(y + 2) = 0

⇒ (y + 2) (y – 1) = 0

⇒ y + 2 = 0 or y – 1 = 0

⇒ y = -2 or y = 1

But x 1/3 = y

∴ x 1/3 = - 2 or x 1/3 = 1

⇒ x = (- 2)3 or x = (1)3

⇒ x = - 8 or x = 1

Hence, roots are -8, 1.