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

Question

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

Tardigrade Admin · Accepted Answer

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}

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

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

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

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

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

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

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

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

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

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