A) - 198
B) 198
C) 99
D) - 99
Correct Answer: B
Solution :
\[{{(x+a)}^{n}}+{{(x-a)}^{n}}=2\,\,\,[{{x}^{n}}+{{\,}^{n}}{{C}_{2}}{{x}^{n-2}}{{a}^{2}}{{+}^{n}}{{C}_{4}}{{x}^{n-4}}{{a}^{4}}+\]\[^{n}{{C}_{6}}{{x}^{n-6}}{{a}^{6}}+.......]\] Here, \[n=6,x=\sqrt{2},a=1\]; \[^{6}{{C}_{2}}=15,{{\,}^{6}}{{C}_{4}}=15,{{\,}^{6}}{{C}_{6}}=1\] \[\therefore \,\,{{(\sqrt{2}+1)}^{6}}{{(\sqrt{2}-1)}^{6}}=2[{{(\sqrt{2})}^{6}}+15.{{(\sqrt{2})}^{4}}.1\]\[+15{{(\sqrt{2})}^{2}}.1+1.1]\] \[=2[8+15\times 4+15\times 2+1]=198\]
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