Question

Solve the following quadratic equations by factorization:

a(x² + 1) - x(a² + 1) = 0

Answer 1

We have been given

a(x² + 1) - x(a² + 1) = 0

ax² - (a² + 1)x + a = 0

ax² - a²x - x + a = 0

ax(x - a) - 1(x - a) = 0

(ax - 1)(x - a) = 0

Therefore,

ax - 1 = 0

ax = 1

x = 1/a

or,

x - a = 0

x = a

Hence, x = 1/a or x = a