olymmath

BALTIC-WAY 1991 Problem 8

    Let a,b,c,d,ea, b, c, d, e be distinct real numbers. Prove that the equation

    (x−a)(x−b)(x−c)(x−d)+(x−a)(x−b)(x−c)(x−e)+(x−a)(x−b)(x−d)(x−e)+(x−a)(x−c)(x−d)(x−e)+(x−b)(x−c)(x−d)(x−e)=0\begin{aligned} & (x-a)(x-b)(x-c)(x-d) \\ & +(x-a)(x-b)(x-c)(x-e) \\ & +(x-a)(x-b)(x-d)(x-e) \\ & +(x-a)(x-c)(x-d)(x-e) \\ & +(x-b)(x-c)(x-d)(x-e)=0 \end{aligned}

    has 4 distinct real solutions.

    Dataset text NuminaMath olympiads. Quoted with source.

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