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max 1/(1 + AP)+1/(1+BP) whn P lies on line AB, with AB=1

Source: Eotvos 1931 p3

September 10, 2024
geometryinequalitiesgeometric inequality

Problem Statement

Let AA and BB be two given points, distance 11 apart. Determine a point PP on the line ABAB such that 11+AP+11+BP\frac{1}{1 + AP}+\frac{1}{1 + BP} is a maximum.
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