QUADRATIC EQUATIONS: For the things of this world cannot be made known without a knowledge of mathematics.
Solve by factorization
a. 4x2 - 4a2x + (a4 - b4) = 0
Ans: 4x2 - 4a2x + (a4-b4) = 0.
4x2 - [2(a2 + b2) + 2 (a2 - b2)] x + (a2 - b2) (a2 + b2) = 0.
⇒ 2x[2x-(a2 + b2)] - (a2 - b2) [2x - (a2 + b2) = 0.
⇒ x = a2 + b2/2 x = a2 - b2/2