Question

The number of real solution(s) of the equation $x^{\frac{2}{3}}+x^{\frac{1}{3}}-2=0$ is/are

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is B $2$

$x^{\frac{2}{3}}+x^{\frac{1}{3}}-2=0$
Let $x^{\frac{1}{3}}=t$
Equation then transforms to
$t^2+t-2=0$
$t^2+2t-t-2=0$
$t(t+2)-1(t+2)=0$
$t=1,-2$

$\therefore x^{1/3}=1$ or $x^{1/3}=-2$
$\therefore$ Equation has two roots .