Question

Solve: x² + 6x – (a² + 2a – 8) = 0.

Answer 1

x² + 6x – (a² + 2a – 8) = 0

⇒ x² + 6x – (a + 4)(a – 2) = 0

⇒ x² + [(a + 4) – (a – 2)]x – (a + 4)(a – 2) = 0

⇒ x² + (a + 4)x – (a – 2)x – (a + 4)(a – 2) = 0 

⇒ x[x + (a + 4)] – (a – 2)[x + (a + 4)] = 0

⇒ [x + (a + 4)][x – (a – 2)] = 0

⇒ x + (a + 4) = 0 or x – (a – 2) = 0 

⇒ x = –(a + 4) or x = (a – 2)

Hence, –(a + 4) and (a – 2) are the roots of the given equation.