Q. If $x^{2/3} - 7x^{1/3} + 10 = 0$, then the value of $x$ is
A) {125}
B) {8}
C) $\varnothing$
D) {125, 8}
Explanation
(d)
Let $\alpha = x^{1/3}$, then it reduces to
$\alpha^{2} - 7\alpha + 10 = 0$
$\Rightarrow \ \ (\alpha - 5)(\alpha - 2) = 0 \Rightarrow \alpha = 5,\ 2$
$\therefore\ \ \alpha^{3} = x\ \ \Rightarrow \ \ \ x = 125$ and 8
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.