SOLUTION: two numbers have a difference of 16. find the numbers if the result of adding their sum and their product is a minimum.

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Question 180304: two numbers have a difference of 16. find the numbers if the result of adding their sum and their product is a minimum.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Call the numbers x and x+-+16
y+=+x+%2B+x+-+16+%2B+x%2A%28x+-+16%29
y+=+x%5E2+-16x+%2B+2x+-+16
y+=+x%5E2+-+14x+-+16
The minimum occurs where x%5Bmin%5D+=+%28-b%29%2F%282a%29 and
the general formula is y+=+ax%5E2+%2B+bx+%2B+c
a+=+1
b+=+-14
x%5Bmin%5D+=+%28-%28-14%29%29%2F%282%2A1%29
x%5Bmin%5D+=+14%2F2
x%5Bmin%5D+=+7
x%5Bmin%5D+-+16+=+-9
The numbers are 7 and -9
check answer:
The minimum value of the sum and product is
y+=+x%5E2+-+14x+-+16
y+=+7%5E2+-+14%2A7+-+16
y+=+49+-+98+-+16
y+=+-65
If I say x+=+6.99,
y+=+6.99%5E2+-+14%2A6.99+-+16
y+=+48.8601+-+97.86+-+16
y+=+-64.9999 not quite a minimum
And if I say x+=+7.01
y+=+7.01%5E2+-+14%2A7.01+-+16
y+=+49.1401+-+98.14+-+16
y+=+-64.9999 not quite a minimum
So, x+=+7 really does give a minimum y