IMO 1970 LL BEL6

Origin: BEL

Problem

Prove that the equation in x n  i=1 bi x −ai = c, bi > 0, a1 < a2 < a3 < \cdot \cdot \cdot < an, has n −1 roots x1, x2, x3, . . . , xn−1 such that a1 < x1 < a2 < x2 < a3 < x3 < \cdot \cdot \cdot < xn−1 < an.