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Find (x+1)^6+(x-1)^6. Hence or otherwise...

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

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To solve the problem, we need to find the value of \((x+1)^6 + (x-1)^6\) and then evaluate \((\sqrt{2}+1)^6 + (\sqrt{2}-1)^6\). ### Step 1: Expand \((x+1)^6\) and \((x-1)^6\) using the Binomial Theorem The Binomial Theorem states that: \[ (a + b)^n = \sum_{r=0}^{n} \binom{n}{r} a^{n-r} b^r \] ...
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