Question

Find two numbers whose difference is 150 and whose product is a minimum.

Answer 1

50, -50.

Answer 2

difference "150" not hundred

Answer 3

75, -75.

Answer 4

ohh yeah thanks

Answer 5

I remember having this question before, and the answer was 50, and -50.

Answer 6

"Let x be the larger number
Let x - 100 be the smaller number
The difference between the two is 100.

The product would be x(x-100) = x² - 100x.

If you take the derivative, you get 2x - 100.

Set this to zero:
2x - 100 = 0
2x = 100
x = 50

Alternatively, if you aren't familiar with calculus, turn the equation into vertex form for a parabola. Do this by completing the square:
x² - 100x = 0

Take the coefficient on the x-term (-100), divide it by 2 (-50), and square it (2500). Add this to both sides:
x² - 100x + 2500 = 2500
(x - 50)² = 2500
(x - 50)² - 2500 = 0

This is vertex form a(x - h)² - k = 0 and the vertex will be at the point x = h or x = 50.

So either way you figure it, the numbers are 50 and -50. The product is -2500 which is minimum." - Puzzling