Question

If `x + 1/x = 3`, find the value of `x^2 + 1/x^2`.

Answer 1

Given: `x + 1/x = 3`

Step-wise calculation:

Square both sides:

`(x + 1/x)^2 = 3^2` which expands to `x^2 + 2 + 1/x^2 = 9`

Rearranging gives:

`x^2 + 1/x^2 = 9 - 2`

`x^2 + 1/x^2 = 7`

So, the value of `x^2 + 1/x^2` is 7.