If `a=(2-sqrt(5))/(2+sqrt(5))` and `b=(2+sqrt(5))/(2-sqrt(5)),` find `a^2-b^2`

Explanation

To find \( a^2 - b^2 \) where \( a = \frac{2 - \sqrt{5}}{2 + \sqrt{5}} \) and \( b = \frac{2 + \sqrt{5}}{2 - \sqrt{5}} \), we can use the identity \( a^2 - b^2 = (a - b)(a + b) \).

### Step 1: Calculate \( a + b \)

First, we need to find \( a + b \):
\[ a + b = \frac{2 - \sqrt{5}}{2 + \sqrt{5}} + \frac{2 + \sqrt{5}}{2 - \sqrt{5}} \]
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