Question

can any one of you solve it urjent for 50 points


#purejaatni ​

Answer 1

Given

$x = \frac{ \sqrt{a + 2b} + \sqrt{a - 2b} }{\sqrt{a + 2b} \: - \: \sqrt{a - 2b}}$

using corponendo and dividando

$\frac{x + 1}{x - 1} \frac{2 \sqrt{a + 2b} }{2 \sqrt{a - 2b} }$

on sqring both side

$\frac{ {x}^{2} + 2x + 1}{ {x}^{2} - 2x + 1} = \frac{a + 2b}{a - 2b}$

again using corponendo and devidendo

$\frac{2( {x}^{2} + 1) }{4x} = \frac{2a}{4b}$

Using Cross multiplication

x^2b + b = ax

So

bx^2 - ax + b= 0

Hence proved

Answer 2

Refer to attachment......✨