 # Find two numbers whose difference is 150 and whose product is a minimum. step 1 if two numbers have a difference of 150, and one of them is x + 150, then the other i The lowest possible product would be -5625 given the numbers 75 and -75.  We can find this by setting the first number as x + 150, which we see in the equation given above. The other number would have to be simply x since it has to have a 150 difference.  Next we'll multiply the numbers together.  x(x+150) x^2 + 150x Now we want to minimize this as much as possible, so we'll find the vertex of this quadratic graph. You can do this by finding the x value as -b/2a, where b is the number attached to x and a is the number attached to x^2 -b/2a = -150/2(1) = -150/2 = -75 So we know one of the values is -75. We can plug that into the equation to find the second.  x + 150  -75 + 150  75

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