Question

Solve $x^{1/3}+\frac{5}{2x^{1/3}}=3\frac{1}{4}$

• A. $-8$ or $-\frac{125}{64}$
• B. $8$ or $\frac{125}{64}$
• C. $-8$ or $\frac{125}{64}$
• D. $8$ or $-\frac{125}{64}$

Answer 1

The correct option is B $8$ or $\frac{125}{64}$

Put $x^{1/3}=y$. Then we have $y+\frac{5}{2y}=\frac{13}{4}$, i.e.,
$4y^2+10=13y$
i.e., $4y^2-13y+10=0$
i.e., $(y-2)(4y-5)=0$
i.e., $y=2$ or $\frac{5}{4}$
i.e., $x^{1/3}=2$ or $\frac{5}{4}$
$\therefore x=8$ or $\frac{125}{64}$