$\"\"$

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

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Let the two numbers are $\"\"$ and $\"\"$ .

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The second number is reciprocal of first number.

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Therefore, $\"\"$ .

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The sum of first number and the second number is minimum.

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Consider the sum function as $\"\"$ .

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Thus, $\"\"$ .

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Apply derivative on each side with respect to $\"\"$ .

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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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$\"\"$ .

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The first number is $\"\"$ .

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The second number is $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ is minimum when $\"\"$ .

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

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$\"\"$

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