Question

If `x + 1/x = 2.5`, the value of x is ______.

पर्याय

• 4

• `5 and 1/5`

• `2 or 1/2`

• `2 and 1/2`

Answer 1

If `x + 1/x = 2.5`, the value of x is `underlinebb(2 or 1/2)`.

Explanation:

Given `x + 1/x = 2.5 = 25/10 = 5/2`

`\implies (x^2 + 1)/x = 5/2`

`\implies` 2(x² + 1) = 5x   ...[Cross multiplying]

`\implies` 2x² + 2 – 5x = 0

`\implies` 2x² – 5x + 2 = 0

`\implies` 2x² – 4x – x + 2 = 0

`\implies` 2x(x – 2) – 1(x – 2) = 0

`\implies` (x – 2)(2x – 1) = 0

Either x – 2 = 0 or 2x – 1 = 0

`\implies` x = 2 or x = `1/2`

`\implies` x = 2 or `1/2`