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max of f(x,y) = \sqrt{(6 -x)(3 + y^2)} + \sqrt{(11 + x)(14 - y^2)}

Source: III - Rioplatense 1993 L3 P4

September 19, 2022

algebrainequalities

Problem Statement

x

and

y

are real numbers such that

6 -x

3 + y^2

11 + x

14 - y^2

are greater than zero. Find the maximum of the function

f(x,y) = \sqrt{(6 -x)(3 + y^2)} + \sqrt{(11 + x)(14 - y^2)}.