Solve the following quadratic equation for x:

9x² – 6b²x – (a⁴ – b⁴) = 0 (CBSE 2015)

Given:

To find: The value of above equation.

Solution: 

 In factorization, we write the middle term of the quadratic equation either as a sum of two numbers or difference of two numbers such that the equation can be factorized.

Consider,



Here,



apply the above formula and solve,

⇒ 9x² – 3(a² + b²)x + 3(a² – b²)x – (a² + b²)(a² – b²) = 0

⇒ 3x(3x – (a² + b²)) + (a² – b²)(3x – (a² + b²)) = 0

⇒ (3x + a² – b²)(3x – (a² + b²) = 0

⇒ x