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If T0, T1, T2,......Tn represent the terms in the expansion of (x+a)n, then the value of (T0-T2+T4-T6+....)2 + (T1-T3+T5-....)2 is (a) (x2 - a2)2(b) (x2 + a2)n(c) (a2 – x2)n(d) None of these

Gokul , 5 Years ago
Grade 11
anser 1 Answers
Aditya Gupta

Last Activity: 5 Years ago

this ques is based on two concepts: namely binomial theorem and complex numbers.
(x+a)n= T0+T1+T2+....+Tn
now we replace a by ia, where i = root(-1)
(x+ia)n= T0 + iT1 – T2 – iT3 + T4 + iT5 – …...= (T0 – T2 + T4 – ….) + i*(T1 – T3 + T5 – ….)
Take modulus both sides and square
 (x2 + a2)n = (T0-T2+T4-T6+....)2 + (T1-T3+T5-....)2
hence option B is correct.

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