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BITSAT2014MathematicsBinomial TheoremActual

If T ₀, ~T ₁, ~T ₂ T _ n represent the terms in the expansion of (x+a)^ n , then ( T ₀- T ₂+ T ₄- . )²+ ( T ₁- T ₃+ T ₅- . . )²=

Options

  1. A(x²+a² )
  2. B(x²+a² )^ n
  3. C(x²+a² )^ 1 / n
  4. D(x²+a² )^ -1 / n

Correct answer

B. (x²+a² )^ n

Step-by-step solution

From the given condition, replacing a by a and -a i respectively, we get (x+a i)^ n = (T₀-T₂+T₄- )+i (T₁-T₃+T₅- . ) ...(i) and (x-a i)^ n = (T₀-T₂+T₄- )-i (T₁-T₃+T₅- ) ...(ii) Multiplying (ii) and (i) we get required result i.e., (x²+a² )^ n = (T₀-T₂+T₄- . )²+ (T₁-T₃+T₅- )²

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