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Question

If the sum of the coefficients in the expansion of (αx22x+1)35 is equal to the sum of the coefficients in the expansion of (xαy)35, then find the value of α.

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Solution

For sum of coefficients in the expansion of (αx22x+1)35 we substitute x=1
We get sum of coefficients of (αx22x+1)35
as (α2+1)35
=(α1)35 ...(i)
Similarly for sum of coefficients of (xαy)35 we substitute x=1 and y=1
We get sum of coefficients (1α)35 ...(ii)
It is given that the sum of coefficients are equal.
Hence (1α)35=(α1)35
α=1

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