Question

Solve $x^{2} -2ax+a ^{2}-b ^{2}$

Answer 1

x²-ax-ax+a²-b² = 0
x(x-a) -a(x-a) -b² =0
(x-a)(x-a) - b² = 0
(x-a)² - b² = 0 (a²-b²=(a+b) ( a-b) )
(x-a+b) (x-a-b) = 0
x-a+b = 0              x-a-b = 0
x = a-b                  x = a+b

Answer 2

Let f(x) =
Then here a = 1, b= -2a and c = (a^2 - b^2)
By the quadratic formula, we have

x = (-b +- √b^2-4ac)/2a
so, x= [-(-2a)+-√(2a)^2 - 4(1)(a^2 - b^2)] / 2
x = (2a +- 2b)/2 =
So x = a+b and a-b