Question

if x =sqrt(a+2b-sqrt(a-2b)/sqrt(a+2b-sqrt(a-2b) prove that bx square - ax + b = 0

Answer 1

x =(√(a+2b)+√(a-2b))/(√(a+2b)-√(a-2b))

use Componendo and dividendo

(x+1)/(x-1) = √(a+2b)/√(a-2b)

square both sides

(x^2 + 2 x + 1)/(x^2-2x + 1) = (a+2b)/(a-2b)

again use Componendo and dividendo

(x^2 + 1)/(2x) = (a)/(2b)

or bx^2 +b = ax
or bx^2 - ax + b = 0

Answer 2

hope the above solution helps you a lot☺