Question

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

Answer 1

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

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

$\frac{10}{\sqrt{xy}}=\frac{10}{3}$

$\sqrt{xy}=3$

$\therefore xy=9$