Question

$\huge \sf \color{red}{\underbrace{Solve}} :$
$\sf \frac{√5 + \sqrt{5-x}}{√5-\sqrt{5-x}} = 3$​

Answer 1

Answer :

$\large \sf x=\frac{15}{4}$

Solution :

$\sf \frac{√5 + \sqrt{5-x}}{√5-\sqrt{5-x}} = 3 \\ \\ \sf \colorbox{skyblue}{Applying \ componendo \ and \ dividendo }\\ \\ \frac{ (√5 + \sqrt{5-x}) + (√5-\sqrt{5-x})}{(√5 + \sqrt{5-x}) - (√5-\sqrt{5-x})} =\frac{3+1}{3-1} \\ \\ \implies \frac{2√5}{2\sqrt{5-x}} = \frac{4}{2} \\ \\ \implies \frac{√5}{\sqrt{5-x}} = 2 \\ \\ \implies √5 =2 \sqrt{5-x} \\ \\ \implies 5=4(5-x) \\ \\ \implies 5 = 20 - 4x \\ \\ \implies 4x= 15 \\ \\ \implies \boxed{ x = \frac{15}{4}}$

Answer 2

Hey mate,

Here is your answer :-

$x = \frac{4}{15}$