Two numbers have a difference of 16. Find the numbers if the result of adding their sum and their product is a minimum.

Question

really long explanation please 🙏🏻

Answer 1

have y-x=16 ,,,y=x+16

have g(x,y)=xy+(y+x)

g(x)=x²+18x+16

with algebra (completing square) or calculus, minimize g(x)

find x=-9

meaning

y=7

Answer 2

S = y² + 18y + 16, as Paul M provided.

S = y² + 18y + 9² + 16 - 9², completion of square

S= (y + 9)² - 65

Vertex at (-9, -65)

The numbers are -9 an -65

Answer 3

x-y=16

Let S=(x+y)+xy....the sum of the sum of the number + the product

Substitute 16+y for x

S=y²+18y+16

Differentiate S with respect to y and set the derivative equal to 0 to get the value for y.