Find the value of `(a^2+sqrt(a^2-1))^4+(a^2-sqrt(a^2-1))^4`.

Explanation

To find the value of \( (a^2 + \sqrt{a^2 - 1})^4 + (a^2 - \sqrt{a^2 - 1})^4 \), we can follow these steps:

### Step 1: Define Variables
Let:
- \( x = a^2 \)
- \( y = \sqrt{a^2 - 1} \)

Then we can rewrite the expression as:
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