Find `(x+1)^6+(x-1)^6`. Hence evaluate `(sqrt(2)+1)^6+(sqrt(2)-1)^6`.

Explanation

To solve the problem, we need to find the value of \((x+1)^6 + (x-1)^6\) and then use that result to evaluate \((\sqrt{2}+1)^6 + (\sqrt{2}-1)^6\).

### Step 1: Use the Binomial Theorem
We start by applying the Binomial Theorem to expand \((x+1)^6\) and \((x-1)^6\).

The Binomial Theorem states that:
\[
(a + b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^k
...