Solve the following quadratic equation by factorisation method: x2 - 2

1.	Solve the following quadratic equation by factorisation method: x2 - 2ax + a2 - b2 = 0.
Answer» Here, Factors of constant term (a²- b²) are (a - b) and (a + b). Also, Coefficient of the middle term = - 2a = - [(a - b) + (a + b)] So, x² - 2ax + a² - b² = 0 => x² - {(a - b) + (a + b)}x + (a - b)(a + b) = 0 => x² - (a - b) x - (a + b) x + (a - b) (a + b) => x{x - (a - b)}- (a + b) {x - (a - b)} = 0 => {x - (a - b)} {x - (a + b)} = 0 => x - (a - b) = 0 or, x - (a + b) = 0 => x = a - b or x = a + b

Solve the following quadratic equation by factorisation method: x2 - 2ax + a2 - b2 = 0.

Answer»

Here, Factors of constant term (a²- b²) are (a - b) and (a + b).

Also, Coefficient of the middle term = - 2a = - [(a - b) + (a + b)]

So, x² - 2ax + a² - b² = 0

=> x² - {(a - b) + (a + b)}x + (a - b)(a + b) = 0

=> x² - (a - b) x - (a + b) x + (a - b) (a + b)

=> x{x - (a - b)}- (a + b) {x - (a - b)} = 0

=> {x - (a - b)} {x - (a + b)} = 0

=> x - (a - b) = 0 or, x - (a + b) = 0

=> x = a - b or x = a + b