If T0, T1, T2, ldots, Tn represent the terms in the expansion of (x+a)n, then (T0=T2+T4-⋅s)2+(T1-T3+T5-⋅s)2=

Question

If T0, T1, T2, ldots, Tn represent the terms in the expansion of (x+a)n, then (T0=T2+T4-⋅s)2+(T1-T3+T5-⋅s)2= (A) (x2+a2) (B) (x2+a2)n (C) (x2+a2)1 / n (D) (x2+a2)-1 / n

Tardigrade Admin · Accepted Answer

(x+a)n= n C0 xn+ n C1 xn-1 a+ n C2 xn-2 a2+ n C3 xn-3 a3+⋅s =T0+T1+T2+T3+⋅s In (1) replacing a by a i (x+a i)n= n C0 xn+ n C1 xn-1 a i+ n C2 xn-2(a i)2+ n C3 xn-3(a i)3+⋅s =( n C0 xn- n C2 xn-2 a2+ n C4 xn-4 a4-⋅s) +i( n C1 xn a- n C3 xn-3 a3+ n C5 xn-5 a5-⋅s) =(T0-T2+T4-⋅s)+i(T1-T3+T5-⋅s) Taking modulus on both sides and squaring |x+a i|2 n= mid(T0-T2+T4-⋅s)+i(T1-T3+T5-⋅s) ⇒ (x2+a2)n=(T0-T2+T4-⋅s)2+(T1-T3+T5-⋅s)2

Q. If $T_{0}, T_{1}, T_{2}, \dots, T_{n}$ represent the terms in the expansion of $(x + a)^{n},$ then $(T_{0} = T_{2} + T_{4} - \dots)^{2} + (T_{1} - T_{3} + T_{5} - \dots)^{2} =$

$(x^{2} + a^{2})$

$(x^{2} + a^{2})^{n}$

$(x^{2} + a^{2})^{1/ n}$

$(x^{2} + a^{2})^{- 1/ n}$

Q. If T0​,T1​,T2​,…,Tn​ represent the terms in the expansion of (x+a)n, then (T0​=T2​+T4​−⋯)2+(T1​−T3​+T5​−⋯)2=

(x2+a2)

(x2+a2)n

(x2+a2)1/n

(x2+a2)−1/n

Q. If $T_{0}, T_{1}, T_{2}, \dots, T_{n}$ represent the terms in the expansion of $(x + a)^{n},$ then $(T_{0} = T_{2} + T_{4} - \dots)^{2} + (T_{1} - T_{3} + T_{5} - \dots)^{2} =$

$(x^{2} + a^{2})$

$(x^{2} + a^{2})^{n}$

$(x^{2} + a^{2})^{1/ n}$

$(x^{2} + a^{2})^{- 1/ n}$