Question

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

Answer 1

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