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Let x and y be positive numbers such that xy=13. Thus, y=13/x. We want to minimize t=x+y=x+13/x. Differentiate t=x+13/x.

t'=1-13x-2

Set this equal to zero.

1-13x-2=0

13x-2=1

x2=13

x=sqrt(13)

Now solve for y:

y=13/x=13/sqrt(13)=sqrt(13)

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