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  • If <img alt="T_0, T_1, T_2, \ldots T_n" src="https://entrancecorner.oncodecogs.com/gif.latex?

If T_0, T_1, T_2, \ldots T_n  represent the terms in the expansion of (x+a)^n, then the value of\left(T_0-T_2+T_4-\ldots .\right)^2+\left(T_1-T_3+T_5-\ldots .\right)^2= 

 

 

 

Option: 1

\left(x^2+a^2\right)


Option: 2

\left(x^2+a^2\right)^n


Option: 3

\left(x^2+a^2\right)^\frac{1}{n}


Option: 4

\left(x^2+a^2\right)^\frac{-1}{n}


Answers (1)

best_answer

From the given condition, replacing a by ai and – ai respectively, we get


(x+a i)^n=\left(T_0-T_2+T_4-\ldots .\right)+i\left(T_1-T_3+T_5-\ldots .\right) ....(i)

and (x-a i)^n=\left(T_0-T_2+T_4-\ldots\right)-i\left(T_1-T_3+T_5-\ldots\right) .....(ii)

Multiplying (ii) and (i) we get required result

i.e. \left(x^2+a^2\right)^n=\left(T_0-T_2+T_4-\ldots .\right)^2+\left(T_1-T_3+T_5-\ldots .\right)^2

Posted by

avinash.dongre

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