If ∀ n ∈ N,(1+x+x2)n=a0+a1x+a2x2+......+a2nx2n where a1a2.....a2n� – InterviewSolution

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1.	If ∀ n ∈ N,(1+x+x2)n=a0+a1x+a2x2+......+a2nx2n where a1a2.....a2n∈Z and a20−a21+a22−a23+.....+a22n=kan then k=
Answer» If $\forall n \in N, (1 + x + x^{2})^{n} = a_{0} + a_{1} x + a_{2} x^{2} + . . . . . . + a_{2 n} x^{2 n} w h e r e a_{1} a_{2} . . . . . a_{2 n} \in Z$ and $a_{0}^{2} - a_{1}^{2} + a_{2}^{2} - a_{3}^{2} + . . . . . + a_{2 n}^{2} = k a_{n}$ then k=

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