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प्रश्न
Evaluate the
(vi) \[\left( 2 + \sqrt{3} \right)^7 + \left( 2 - \sqrt{3} \right)^7\]
उत्तर
(vi) \[(2 + \sqrt{3} )^7 + (2 - \sqrt{3} )^7 \]
\[ = 2[ ^{7}{}{C}_0 \times 2^7 \times (\sqrt{3} )^0 + ^{7}{}{C}_2 \times 2^5 \times (\sqrt{3} )^2 + ^{7}{}{C}_4 \times 2^3 \times (\sqrt{3} )^4 +^{7}{}{C}_6 \times 2^1 \times (\sqrt{3} )^6 ]\]
\[ = 2[128 + 21 \times 32 \times 3 + 35 \times 8 \times 9 + 7 \times 2 \times 27]\]
\[ = 2[128 + 2016 + 2520 + 378]\]
\[ = 2 \times 5042 = 10084\]
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\[= ^{5}{}{C}_0 (2x )^5 (3y )^0 +^{5}{}{C}_1 (2x )^4 (3y )^1 + ^{5}{}{C}_2 (2x )^3 (3y )^2 + ^{5}{}{C}_3 (2x )^2 (3y )^3 + ^{5}{}{C}_4 (2x )^1 (3y )^4 +^{5}{}{C}_5 (2x )^0 (3y )^5\]
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