Question

Solve the following quadratic equation for x: x² – 2ax – (4b² – a²) = 0

Answer 1

x² – 2ax – (4b² – a²) = 0
⇒ x² + (2b – a)x – (2b + a)x – (4b² – a²) = 0
⇒ x(x + 2b – a) – (2b + a)(x + 2b – a) = 0
⇒ (x + 2b – a)(x – 2b – a) = 0
⇒ (x + 2b – a) = 0, (x – 2b – a) = 0
∴ x = a − 2b, a + 2b