MathDB

8.5

Part of 2001 All-Russian Olympiad Regional Round

Problems(1)

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

Source:

9/25/2024
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.
algebra