A) \[({{x}^{2}}+{{a}^{2}})\]
B) \[{{({{x}^{2}}+{{a}^{2}})}^{n}}\]
C) \[{{({{x}^{2}}+{{a}^{2}})}^{1/n}}\]
D) \[{{({{x}^{2}}+{{a}^{2}})}^{-1/n}}\]
Correct Answer: B
Solution :
From the given condition, replacing a by ai and ? ai respectively, we get \[{{(x+ai)}^{n}}=({{T}_{0}}-{{T}_{2}}+{{T}_{4}}-....)+i({{T}_{1}}-{{T}_{3}}+{{T}_{5}}-....)\] ....(i) and \[{{(x-ai)}^{n}}=({{T}_{0}}-{{T}_{2}}+{{T}_{4}}-....)-i({{T}_{1}}-{{T}_{3}}+{{T}_{5}}-....)\] ......(ii) Multiplying (ii) and (i) we get required result i.e. \[{{({{x}^{2}}+{{a}^{2}})}^{n}}={{({{T}_{0}}-{{T}_{2}}+{{T}_{4}}-....)}^{2}}+{{({{T}_{1}}-{{T}_{3}}+{{T}_{5}}-....)}^{2}}\]
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