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Not This Type of Inequality

Source: Indonesia RMO 2022, Essay No 3

August 24, 2022
IndonesiaRMO2022algebrainequalities

Problem Statement

It is known that xx and yy are reals satisfying 5x2+4xy+11y2=3. 5x^2 + 4xy + 11y^2 = 3. Without using calculus (differentials/integrals), determine the maximum value of xyāˆ’2x+5yxy - 2x + 5y.
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