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Max of (xy+1)(yz+1)(zx+1)

Source: Turkey EGMO TST 2020 P6

February 6, 2020
inequalitiesalgebraTurkeyHigh school olympiadinequalities proposed

Problem Statement

x,y,zx,y,z are positive real numbers such that: xyz+x+y+z=6xyz+x+y+z=6 xyz+2xy+yz+zx+z=10xyz+2xy+yz+zx+z=10 Find the maximum value of: (xy+1)(yz+1)(zx+1)(xy+1)(yz+1)(zx+1)
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