Question

Solve for y in the following equation:
$y^{2/3}-2y^{1/3}=15$

• A. -27 and 125
• B. -125 and 27
• C. -125 and -27
• D. None of These

Answer 1

The correct option is A -27 and 125

We have,
$y^{\frac{2}{3}}-2y^{\frac{1}{3}}=15$
Let $y^{\frac{1}{3}}=p$
So, we get,
$p^2-2p=15$
$\Rightarrow p^2-2p-15=0$
$\Rightarrow p^2-5p+3p-15=0$
$\Rightarrow p(p-5)+3(p-5)=0$
$\Rightarrow (p-5)(p+3)=0$
$\Rightarrow p=5$ or $p=-3$
$\Rightarrow y^{\frac{1}{3}}$ = 5 or $y^{\frac{1}{3}}=-3$
$\Rightarrow y=5^3=125$ or $y=(-3{)}^3=-27$
So, correct option is a.