Question 1125299
Both numbers,  {{{10*sqrt(2)}}}.


{{{system(xy=200,A=x+y)}}}


{{{y=200/x}}}
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{{{A=x+200/x}}}

{{{dA/dx=1-200/x^2}}}

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{{{1-200/x^2=0}}}

{{{(x^2-200)/x^2=0}}}

{{{x^2-200=0}}}

{{{x^2=200}}}

{{{x=10*sqrt(2)}}}
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{{{y=200/x}}}

{{{y=200/(10*sqrt(2))}}}

.