Question

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

Answer 1

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