Question

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

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

Answer 1

Answer: (D)

$9$

$\sqrt{\frac{x}{y}}+\sqrt{\frac{y}{x}}=\frac{10}{3}$
$\Rightarrow \frac{\sqrt{x}}{\sqrt{y}}+\frac{\sqrt{y}}{\sqrt{x}}=\frac{10}{3}$
$\Rightarrow \frac{{\left(\sqrt{x}\right)}^2+{\left(\sqrt{y}\right)}^2}{\sqrt{y}.\sqrt{x}}=\frac{10}{3}\Rightarrow \frac{x+y}{\sqrt{xy}}=\frac{10}{3}$
$\Rightarrow \frac{10}{\sqrt{xy}}=\frac{10}{3}\Rightarrow \sqrt{xy}=3\Rightarrow xy=9$