quadratic equations for the things of

Question

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