Find two numbers whose difference is 200 and whose product is a minimum

X-y=200

xy=mn

so

first equation times - 1 and add x both sides

y=x-200

sub that for y in other equation

x (x-200) = min

x²-200x=min

take deritivive

2x-200=min

find where it equals 0

2x-200=0

2x=200

x=100

y=x-200

y=100-200

y=-100

the numbers aer 100 and - 100