Solve for `x`: `(5+2sqrt(6))^[x^2-3]+(5-2sqrt(6))^[x^2-3]=10`

Explanation

To solve the equation \((5 + 2\sqrt{6})^{x^2 - 3} + (5 - 2\sqrt{6})^{x^2 - 3} = 10\), we can follow these steps:

### Step 1: Substitute for \(p\)
Let \(p = (5 + 2\sqrt{6})^{x^2 - 3}\). Then, we can express the equation as:
\[ p + \frac{1}{p} = 10 \]

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