Determine two numbers whose difference is -4 and whose product is a minimum. Let x be one number and let y be the other.

There is another question similar to this but with maximum instead of minimum, the concept should be the same, right?

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- Jan 2nd 2010, 12:30 PMbrownjoviFinding two unknown numbers
Determine two numbers whose difference is -4 and whose product is a minimum. Let x be one number and let y be the other.

There is another question similar to this but with maximum instead of minimum, the concept should be the same, right? - Jan 2nd 2010, 12:37 PMskeeter
- Jan 2nd 2010, 05:10 PMbrownjovi
- Jan 2nd 2010, 06:19 PMSabo
I am a newbie myself, but I think that one way to solve this is to think something along these lines.

If y is negative, the product y(y-4) will be positive.

If y is positive, there will be a few numbers for which the product y(y-4) is negative, and some for which the product will be positive.

In this particular case it is easy to manually figure out for which values of y the product will be negative, since there are only so many positive values of y for which (y-4) will remain negative. - Jan 2nd 2010, 08:39 PMDrexel28
If we consider completing the square gives which when we may clearly see that so that it attains it's minimum at . Geometrically all we did was find the vertex of the parabola.

- Jan 3rd 2010, 12:49 AMHallsofIvy
Actually, no. There will be an

**infinite**wet of numbers for which the product y(y- 4) is negative. You cannot*assume*the number will be a whole number. Completing the square, as Drexel28 suggested, will always give you the minimum or maximum point (vertex of the parabola) of a quadratic function.

Quote:

In this particular case it is easy to manually figure out for which values of y the product will be negative, since there are only so many positive values of y for which (y-4) will remain negative.

- Jan 3rd 2010, 01:57 AMSabo
Right. Stuck in integer land. =/