$\"\"$

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

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

$\"\"$ .

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

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

$\"\"$

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

$\"\"$

$\"\"$ .

Equate $\"\"$ to zero. \ \

$\"\"$

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

$\"\"$ .

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

$\"\"$

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