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cx^2 - bx + a >cx - b if ax^2+bx+c >cx

Source: Flanders Math Olympiad 2011 p1

December 24, 2022
algebrainequalitiestrinomial

Problem Statement

Given are three numbers a,b,c∈R−{0}a, b, c \in R-\{0\}. The parabola with equation y=ax2+bx+cy = ax^2+bx+c lies above the line y=cxy = cx. Prove that the parabola with equation y=cx2−bx+ay = cx^2 - bx + a lies above the line y=cx−by = cx - b.
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