Question

The roots of the equation $x^{\frac{2}{3}}+x^{\frac{1}{3}}-2$ = 0 are

• A. 1,4
• B. 1,-4
• C. 1,-8
• D. 1, 8

Answer 1

The correct option is C

1,-8

$x^{\frac{2}{3}}+x^{\frac{1}{3}}-2$ = 0 ⇒ $(x^{\frac{1}{3}}{)}^2+x^{\frac{1}{3}}-2$ = 0

let a = $x^3$, then $a^2+a-2$ = 0 ⇒ a = 1, -2

Hence x = 1, - 8 (by a = $x^{\frac{1}{3}}$).