Question

Solve the following equation using quadratic formula:

x² – 4x + 1 = 0

Answer 1

Comparing equation x² – 4x + 1 = 0 with ax² + bx + c = 0, we get :

a = 1, b = –4 and c = 1

By formula,

`x = (-b ± sqrt(b^2 - 4ac))/(2a)`

Substituting values we get:

⇒ `x = (-(-4) ± sqrt((-4)^2 - 4 xx 1 xx 1))/(2 xx 1)`

= `(4 ± sqrt(16 - 4))/2`

= `(4 ± sqrt(12))/2`

= `(4 ± sqrt(4 xx 3))/2`

= `(4 ± 2sqrt(3))/2`

= `(2(2 ± sqrt(3)))/2`

= `2 ± sqrt(3)`

= `2 + sqrt(3)` or `2 - sqrt(3)`

Hence, `x = {2 + sqrt(3), 2 - sqrt(3)}`.