QUADRATIC EQUATIONS: For the things of this world cannot be made known without a knowledge of mathematics.
Solve by factorization
a. 4x^{2} - 4a^{2}x + (a^{4} - b^{4}) = 0
Ans: 4x^{2} - 4a^{2}x + (a^{4}-b^{4}) = 0.
4x^{2} - [2(a^{2} + b^{2}) + 2 (a^{2} - b^{2})] x + (a^{2} - b^{2}) (a^{2} + b^{2}) = 0.
⇒ 2x[2x-(a^{2} + b^{2})] - (a^{2} - b^{2}) [2x - (a^{2} + b^{2}) = 0.
⇒ x = a^{2} + b^{2}/2 x = a^{2} - b^{2}/2