To find the answer you must derive an equation with one variable so, set x-y=100 thus y=100-x now substitute into your product equation
x(100-x) then differentiate with respect to x
d/dx= 100-2x
then set the equation equal to zero and solve for x
x= 50 and note that some may think the minimum is 0 but in fact 50*-50= -2500 which is far less than zero.
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-76 and 76 whose product is -5776.
11
-5 * 5 = -25
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Suppose the smaller of the two numbers is x. Then the other number is x+22. Their product is x*(x+22) = x2 + 22x This has a minimum when 2x = -22 or x = -11. When x = 11, the two numbers are -11 and 11 with a product of -121.