Question

Prove that if a+b is non zero, then a (x-a)=2ab-b (x-b)as a solution x=a+b

Answer 1

$a(x - a) = 2ab - b(x - b)$
$ax - {a}^{2} = 2ab - bx + {b}^{2}$
$ax + bx = {a}^{2} + 2ab + {b}^{2}$
$x(a + b) = {(a + b)}^{2}$
$x(a + b) = (a + b)(a + b)$
$x = a + b$
proved

Answer 2

It is easy , please read identities from class 9 chapter 2 ncert