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Let X be the lower number.
The problem is: minimize X(X+8).
Let Y=X(X+8)=X2+8X.
The vertex of this parabola is the minimum since it points up.
The X-coordinate of the vertex is -8/2 = -4.
So the minimum product is -4*4 = -16.
Note the two numbers here are -4 and 4.
Verify (using calculus)
dY/dX = 2X + 8 = 0 iff X = -8/2 = -4.
, implies Y = -16.
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