Question

The number of solution of the equation $x^{\frac{2}{3}}+x^{\frac{1}{3}}-2=0$ is

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is A 1

$x^{2/3}+x^{1/3}-2=0$

$x^{1/3}=y$

$\therefore y^2+y-2=0$

$y^2+2y-y-2=0$

$(y-1)(y+2)=0$

$\Rightarrow y=-2$ or $y=1$

$\Rightarrow x^{1/3}=-2$ or $1$

$x=(-2{)}^3$ or $1^3$

$x=-8$ or $1$