If `vec a` is a unit vector and `(vec x - vec a).(vec x + vec a)=8`, then find `|vec x|`

Explanation

To solve the problem, we start with the given equation:

\[ (\vec{x} - \vec{a}) \cdot (\vec{x} + \vec{a}) = 8 \]

### Step 1: Expand the dot product
Using the distributive property of the dot product, we can expand the left-hand side:
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