Question

If $\sqrt{\frac{x}{y}}+\sqrt{\frac{y}{x}}=\frac{10}{3}$ and $x+y=10$, find the value of $xy.$

• A. $36$
• B. $24$
• C. $16$
• D. $9$

Answer 1

Answer: (D)

$9$

$\sqrt{\frac{x}{y}}+\sqrt{\frac{y}{x}}$ $=\frac{10}{3}$

$\frac{x+y}{\sqrt{xy}}=\frac{10}{3}$

as given above $x+y=10$

$\sqrt{xy}=3$

squaring both sides

$xy=9$