Question

Solve the following quadratic equation for x : 4x² − 4a²x + (a⁴ − b⁴) =0.

Answer 1

We have

4x²−4a²x+(a⁴−b⁴)=0

⇒ (4x²−4a²x+a⁴)−b⁴=0

⇒[(2x)²−2(2x)(a)+(a²)²]−b⁴=0

⇒(2x−a²)²−(b²)²=0

⇒(2x−a²+b²)(2x−a²−b²)=0

⇒2x−a²+b²=0  or  2x−a²−b²=0

⇒2x=a²−b²  or  2x=a²+b²

`=>x=(a^2-b^2)/2 " or " x = (a^2+b^2)/2`