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|ax+b|+|cx+d|=|ex+f| - All-Russian MO 2001 Regional (R4) 8.5

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September 25, 2024
algebra

Problem Statement

Let a,b,c,d,ea, b, c, d, e and ff be some numbers, and a⋅c⋅e≠0 a \cdot c \cdot e \ne 0.It is known that the values of the expressions ∣ax+b∣+∣cx+d∣|ax+b|+|cx+d| and ∣ex+f∣|ex+f| equal at all values of xx. Prove that ad=bcad = bc.
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