Question

Solve the following equation by factorization:

`x^2 - (1 + sqrt(2))x + sqrt(2) = 0`

Answer 1

`x^2 - (1 + sqrt(2))x + sqrt(2) = 0`

⇒ `x^2 - x - sqrt(2)x + sqrt(2) = 0`

⇒ `(x - 1) - sqrt(2) (x - 1)= 0`

⇒ `(x - 1) (x - sqrt(2)) = 0`

Either x – 1 = 0,

Then x = 1

or

`x - sqrt(2) = 0`,

Then x = `sqrt(2)`

Hence x = 1, `sqrt(2)`.

Answer 2

Given,

⇒ `x^2 - (1 + sqrt(2))x + sqrt(2) = 0`

⇒ `x^2 - 1x - sqrt(2)x + sqrt(2) = 0`

⇒ `x(x - 1) - sqrt(2)(x - 1) = 0`

⇒ `(x - sqrt(2))(x - 1) = 0`

⇒ `(x - sqrt(2)) = 0` or (x – 1) = 0   ...[Using zero-product rule]

⇒ `x = sqrt(2)` or x = 1

Hence, `x = {1, sqrt(2)}`.