Find the quadratic equation with rational coefficients whose one root is `1//(2+sqrt(5))dot`

Explanation

To find the quadratic equation with rational coefficients whose one root is \( \frac{1}{2 + \sqrt{5}} \), we will follow these steps:

### Step 1: Rationalize the given root
The given root is \( \alpha = \frac{1}{2 + \sqrt{5}} \). To rationalize it, we multiply the numerator and the denominator by the conjugate of the denominator:

\[ \alpha = \frac{1}{2 + \sqrt{5}} \cdot \frac{2 - \sqrt{5}}{2 - \sqrt{5}} = \frac{2 - \sqrt{5}}{(2 + \sqrt{5})(2 - \sqrt{5})} \]
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