IMO 1989 LL GBR28

Let b1, b2, . . . , b1989 be positive real numbers such that the

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IMO 1989 LL GBR28

Origin: GBR

Problem

Let b1, b2, . . . , b1989 be positive real numbers such that the equations xr−1 −2xr + xr+1 + brxr = 0 (1 \leqr \leq1989) have a solution with x0 = x1990 = 0 but not all of x1, . . . , x1989 are equal to zero. Prove that b1 + b2 + \cdot \cdot \cdot + b1989 \geq 995.