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

Source: Russian Regional Olympiad 2010 10.5

August 24, 2024
algebrainequalities

Problem Statement

Non-zero numbers a,b,ca, b, c are such that ax2+bx+c>cxax^2+bx+c > cx for any xx. Prove that cx2−bx+a>cx−bcx^2-bx + a > cx-b for any xx.
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