$\"\"$

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The product is $\"\"$ and sum is a minimum.

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

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

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$\"\"$

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Let the sum of two numbers is $\"\"$ .

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

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$\"\"$

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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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Power rule of derivative : $\"\"$ .

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$\"\"$

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$\"\"$

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Equate the derivative function to zero.

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$\"\"$

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

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$\"\"$

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