Question

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

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

Answer 1

The correct option is D $1,-8$

The given equation is $x^{2/3}+x^{1/3}-2=0$
Put $x^{1/3}=y$, then $y^2+y-2=0$
$\Rightarrow (y-1)(y+2)=0\Rightarrow y=1$ or $y=-2$
$\Rightarrow x^{1/3}=1$ or $x^{1/3}=-2$
$\therefore x=(1{)}^3=1$ or $x=(-2{)}^3=-8$
Hence, the real root of the given equation are $1$ & $-8$.