Question

If `x + 1/x = 4`, find the value of `x^2 + 1/x^2`.

Answer 1

Given: `x + 1/x = 4`

Step-wise calculation:

1. Square both sides:

`(x + 1/x)^2 = 4^2`

2. Expanding the left side:

`x^2 + 2 + 1/x^2 = 16`

3. Subtract 2 from both sides to isolate `x^2 + 1/x^2`:

`x^2 + 1/x^2 = 16 - 2`

`x^2 + 1/x^2 = 14`