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

Answer: (C)

$1,-8$

Given equation is $x^{\frac{2}{3}}+x^{\frac{1}{3}}-2=0$
Let $x^{1/3}=t$
$\Rightarrow t^2+t-2=(t+2)(t-1)=0$
$\Rightarrow x^{\frac{1}{3}}=-2$ or $x^{\frac{1}{3}}=1$
$\therefore x=-8$ or $x=1$
Hence, option C .