Question

If $\frac{\sqrt{5+x}+\sqrt{5-x}}{\sqrt{5+x}-\sqrt{5-x}}=4$, then value of $x$ is

• A. $\frac{20}{17}$
• B. $\frac{18}{7}$
• C. $\frac{40}{17}$
• D. $\frac{43}{7}$

Answer 1

The correct option is C $\frac{40}{17}$

$\frac{\sqrt{5+x}+\sqrt{5-x}}{\sqrt{5+x}-\sqrt{5-x}}=4$
Applying componendo and dividendo, we get
$\Rightarrow \frac{2\sqrt{5+x}}{2\sqrt{5-x}}=\frac{5}{3}$
Squaring both sides
$\Rightarrow \frac{5+x}{5-x}=\frac{25}{9}$
$\Rightarrow x=\frac{40}{17}$