If `x+1/x=sqrt(5)` , find the values of `x^2+1/(x^2)` and `x^4+1/(x^4)`

Explanation

To solve the problem, we need to find the values of \( x^2 + \frac{1}{x^2} \) and \( x^4 + \frac{1}{x^4} \) given that \( x + \frac{1}{x} = \sqrt{5} \).

### Step 1: Find \( x^2 + \frac{1}{x^2} \)

We start with the equation:

\[
x + \frac{1}{x} = \sqrt{5}
...