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robinjean
The sum of two nonnegative numbers is 20. Find the numbers if the sum of their squares is as large as possible; as small as possible.
x+y=20 A=x^2+y^2 A=x^2+(20-x)^2 A=2x^2-40x+400 A'=4x-40=0 x=10 y=10
10^2+10^2=200 is min. 20^2+0^=400 max