CAT 2006 — QA Question 15

$x^{\frac{2}{3}}+x^{\frac{1}{3}}-2\le 0$   ...(1)

Put y = x^1/3

Then equation (1) becomes y² + y – 2 ≤ 0

(y + 2)(y – 1) ≤ 0

–2 ≤ y ≤ 1

$-2\le x^{\frac{1}{3}}\le 1$

–8 ≤ x ≤ 1

Hence, option (a).