Question

The roots of the equation `x + 1/x = 3` are:

पर्याय

• `(2 ± sqrt(5))/2`

• `(3 ± sqrt(5))/2`

• `(1 ± sqrt(3))/2`

• none of these

Answer 1

`bb((3 ± sqrt(5))/2)`

Explanation:

Given,

`x + 1/x = 3`

Multiplying whole equation by x, we get:

⇒ `(x^2 + 1)/x = 3`

⇒ x² + 1 = 3x

⇒ x² – 3x + 1 = 0

Comparing equation x² – 3x + 1 = 0 with ax² + bx + c = 0, we get:

a = 1, b = –3 and c = 1.

By formula,

`x = (-b ± sqrt(b^2 - 4ac))/(2a)`

Substituting values we get:

⇒ `x = (-(-3) ± sqrt((-3)^2 - 4 xx 1 xx 1))/(2 xx 1)`

= `(3 ± sqrt(9 - 4))/2`

= `(3 ± sqrt(5))/2`