$\"\"$

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The sum of two numbers is $\"\"$ .

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Let $\"\"$ and $\"\"$ be two positive numbers such that $\"\"$ .

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$\"\"$ .

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Find the product function.

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The product of two numbers is $\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$ .

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Differentiate on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$ .

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Find the critical numbers by equating derivative to zero.

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$\"\"$

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$\"\"$

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$\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$ .

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$\"\"$

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$\"\"$ is maximum when $\"\"$ .

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Therefore, the two numbers are $\"\"$ , $\"\"$ .

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$\"\"$

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The two numbers are $\"\"$ , $\"\"$ .