Find `| vec a|`and `| vec b|`, if `( vec a+ vec b)dot(( vec a- vec b))=8`and `|vec a|=8 | vec b|`

Explanation

To solve the problem, we need to find the magnitudes of vectors \( \vec{a} \) and \( \vec{b} \) given the equations:

1. \( (\vec{a} + \vec{b}) \cdot (\vec{a} - \vec{b}) = 8 \)
2. \( |\vec{a}| = 8 |\vec{b}| \)

### Step 1: Expand the dot product

Using the property of the dot product, we can expand the left-hand side of the first equation:
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