We have a binomial expansion $(x+y)^n$ , where $x,y,n$ are all some real numbers and are unknown. (n$\in$ I), (x, y ≠ 0)
And we know the numerical values of $(r-2)$th, (r)th and $(r+2)$th terms of the expansion (suppose them to be A,B,C respectively) (numerical value of r is given) . So, will there be only a unique such expansion (if possible) or can there be two such expansions,i.e., we get two values of n.
The expansion will not be unique.
As an simple counterexample, $(x-y)^n$ will have every other term same as $(x + y)^n$, if $r$ is odd.
Two polynomials are the same if and only if all terms are identical. Three terms will not be enough in general.