If `lim_(x to a) (x^(7) + a^(7))/(x + a) = 7`, find the value of a.

Explanation

To solve the limit problem, we start with the expression given:

\[ \lim_{x \to a} \frac{x^7 + a^7}{x + a} = 7 \]

### Step 1: Rewrite the Limit Expression
We can rewrite the limit expression by factoring the numerator. We can use the identity for the sum of cubes, but in this case, we will use the fact that:
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