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प्रश्न
Evaluate the
(iv) \[\left( \sqrt{2} + 1 \right)^6 + \left( \sqrt{2} - 1 \right)^6\]
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उत्तर
(iv) \[(\sqrt{2} + 1 )^6 + (\sqrt{2} - 1 )^6 \]
\[ = 2[^{6}{}{C}_0 (\sqrt{2} )^6 +^{6}{}{C}_2 (\sqrt{2} )^4 + ^{6}{}{C}_4 (\sqrt{2} )^2 + ^{6}{}{C}_6 (\sqrt{2} )^0 ]\]
\[ = 2[8 + 15 \times 4 + 15 \times 2 + 1)\]
\[ = 2 \times 99 = 198\]
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