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प्रश्न
Evaluate the
(iv) \[\left( \sqrt{2} + 1 \right)^6 + \left( \sqrt{2} - 1 \right)^6\]
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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संबंधित प्रश्न
Using binomial theorem, write down the expansions :
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\[= ^{5}{}{C}_0 (2x )^5 (3y )^0 +^{5}{}{C}_1 (2x )^4 (3y )^1 + ^{5}{}{C}_2 (2x )^3 (3y )^2 + ^{5}{}{C}_3 (2x )^2 (3y )^3 + ^{5}{}{C}_4 (2x )^1 (3y )^4 +^{5}{}{C}_5 (2x )^0 (3y )^5\]
\[= 32 x^5 + 5 \times 16 x^4 \times 3y + 10 \times 8 x^3 \times 9 y^2 + 10 \times 4 x^2 \times 27 y^3 + 5 \times 2x \times 81 y^4 + 243 y^5 \]
\[ = 32 x^5 + 240 x^4 y + 720 x^3 y^2 + 1080 x^2 y^3 + 810x y^4 + 243 y^5 \]
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