SOLUTION: Two numbers have a difference of 24 . Find the numbers if the result of adding their sum and their product is a minimum.
Can you please help me out? Thanks so much in advance:)
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Question 788876: Two numbers have a difference of 24 . Find the numbers if the result of adding their sum and their product is a minimum.
Can you please help me out? Thanks so much in advance:)
Can you also please show the steps it would really help me understand:) Thank-you
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
= the smallest of the two numbers
= the other number
= their sum
= their product
= the result of adding their sum and their product.
We need to find the value of that minimizes the y value for that function.
Let's simplify that expression:
As for all and for ,
for all and is the minimum for
So and are the two numbers we were looking for.
WITH FORMULAS:
THe formulas you were given may be slightly different.
You were probably given as general formula for the quadratic function, and
as the formula to find the x-coordinate of the minimum.
In this case, , , and
is the x-coordinate of the minimum.
The two numbers are and
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