A) 5
B) 6
C) 7
D) 8
Correct Answer: C
Solution :
We know that,\[{{(a+b)}^{5}}+{{(a-b)}^{5}}\] \[=2{{[}^{5}}{{C}_{0}}{{a}^{5}}{{+}^{5}}{{C}_{2}}{{a}^{3}}{{b}^{2}}{{+}^{5}}{{C}_{4}}a{{b}^{4}}]\] \[=2[{{a}^{5}}+10{{a}^{3}}{{b}^{2}}+5a{{b}^{4}}]\] \[\therefore \]\[{{[x+{{({{x}^{3}}-1)}^{1/2}}]}^{5}}+{{[x-{{({{x}^{3}}-1)}^{1/2}}]}^{5}}\] \[=2[{{x}^{5}}+10{{x}^{3}}({{x}^{3}}-1)+5x{{({{x}^{3}}-1)}^{2}}]\] \[=2[{{x}^{5}}+10{{x}^{6}}-10{{x}^{3}}+5{{x}^{7}}+5x-10{{x}^{4}}]\] Therefore, the given expression is a polynomial of degree 7.You need to login to perform this action.
You will be redirected in
3 sec