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Maximal and minimal value of x+2y

Source: Bulgarian Spring Tournament 2024 10.1

March 31, 2024
algebrainequalities

Problem Statement

The reals x,yx, y satisfy x(x−6)≤y(4−y)+7x(x-6)\leq y(4-y)+7. Find the minimal and maximal values of the expression x+2yx+2y.
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