$\"\"$

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The sum of first number and twise the second number is $\"\"$ and product is a maximum.

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

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The sum of first number and twise the second number is $\"\"$ .

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$\"\"$ .

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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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Equate derivative function 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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Therefore two numbers are $\"\"$ and $\"\"$ .

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$\"\"$

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