Question

Using properties of proportion solve:
$\frac{\sqrt{x+5}+\sqrt{x-16}}{\sqrt{x+5}-\sqrt{x-16}}=\frac{7}{3}$

Answer 1

$\frac{\sqrt{x+5}+\sqrt{x-16}}{\sqrt{x+5}-\sqrt{x-16}}=\frac{7}{3}$

$\Rightarrow \frac{2\sqrt{x+4}}{2\sqrt{x-16}}=\frac{10}{4}$

$\Rightarrow \frac{\sqrt{x+4}}{\sqrt{x-16}}=\frac{5}{2}$

$\Rightarrow 4(x+4)=25(x-16)$

$\Rightarrow 4x+16=25x-400$

$\Rightarrow 416=21x$

$\Rightarrow x=\frac{416}{21}$