Solve each of the following quadratic equations:
x2 - 4ax - b2 + 4a2 = 0
x2 - 4ax - b2 + 4a2 = 0
x2 - 4ax – ((b)2 – (2a)2) = 0
{using a2 - b2 = (a + b)(a - b)}
x2 - (b + 2a)x + (b - 2a)x - (b + 2a)(b - 2a) = 0
⇒ x [x - (b + 2a)] + (b - 2a) [x - (b + 2a)] = 0
⇒ [x - (b + 2a)] [x + (b - 2a)] = 0
⇒ [x - (b + 2a)] = 0 or [x + (b - 2a)] = 0
⇒ x = (b + 2a) or x = - (b - 2a)
⇒ x = (2a + b) or x = (2a - b)
Hence the roots of equation are (2a + b) or (2a - b)