Question

If `x+1/x=sqrt5`, find the value of `x^2+1/x^2`?

Answer 1

`3`

Explanation:

We square both sides.

`(x + 1/x)^2 = sqrt(5)^2`

`x^2 + 2 + 1/x^2 = 5`

`x^2 + 1/x^2 = 3`

Hopefully this helps!

Answer 2

3

Explanation:

`x+ 1/x = sqrt(5) -> (x+1/x)^2 = sqrt(5)^2`
`x^2+(2 * x * 1/x) + (1/x)^2 = 5`
`x^2+2x/x+1/x^2 = 5`
`x^2+2+1/x^2=5`
`x^2+1/x^2 = 5-2 = 3`