A) 23
B) 24
C) 18
D) 21
Correct Answer: B
Solution :
\[{{\left( x+\sqrt{{{x}^{3}}-1} \right)}^{6}}+{{\left( x+\sqrt{{{x}^{3}}-1} \right)}^{6}}\]\[=2{{(}^{6}}{{C}_{0}}{{x}^{6}}{{+}^{6}}{{C}_{2}}{{x}^{4}}({{x}^{3}}-1){{+}^{6}}{{C}_{4}}.{{x}^{2}}{{({{x}^{3}}-1)}^{2}}\]\[{{+}^{6}}{{C}_{6}}{{({{x}^{2}}-1)}^{3}})\] |
Terms with even powers of \[x\] |
\[=2{{(}^{6}}{{C}_{0}}.{{x}^{6}}{{-}^{6}}{{C}_{2}}.{{x}^{4}}{{+}^{6}}{{C}_{4}}{{x}^{2}}{{+}^{6}}{{C}_{4}}{{x}^{8}}{{+}^{6}}{{C}_{6}}(-1-3{{x}^{6}})\] |
coefficients\[=2{{(}^{6}}{{C}_{0}}{{-}^{6}}{{C}_{2}}{{+}^{6}}{{C}_{4}}{{+}^{6}}{{C}_{4}}{{-}^{6}}{{C}_{6}}-{{3.}^{6}}{{C}_{6}})\] |
\[=2(15-3)=24.\] |
You need to login to perform this action.
You will be redirected in
3 sec