Question

Solve the quadratic equation: x² – 2ax + (a² – b²) = 0 for x.

Solve by completing the square:

x² – 2ax + (a² – b²) = 0

Answer 1

We have, x² – 2ax + (a² – b²) = 0

⇒ x² – ((a + b) + (a – b))x + (a² – b²) = 0

⇒ x² – (a + b)x – (a – b)x + (a + b) (a – b) = 0   ...[∵ a² – b² = (a + b) (a – b)]

⇒ x(x – (a + b)) – (a – b) (x – (a + b)) = 0

⇒ (x – (a + b)) (x – (a – b) = 0

⇒ x = a + b, a – b