+0

# (Grade 11 Pre Calc) Two numbers have a difference of 18. Does their product have a maximum or a minimum value? Determine the value of 2 nums

0
59
2

The equation I got from that is (18+x)(18+x) or (x-18)(x-18) - both not giving me the right answer :( The answer is minimum; -81; -9 and 9

Mar 27, 2020

#1
+1970
-1

I'm in elementary school, so I'm not so good at this. But I will try to help.

x=first number

x+18=second number

Their product will have a minimum, since you are supposed to do (x+18)(x-18)

I am not 100% if this is correct.

Hope this helped, though!

Mar 27, 2020
#2
+111330
+1

Let's look at this from a slightly different perspective

Let the  interger  in   the exact  middle of the two integers   (their average) =  x

Then the lesser  number =   (x - 9)

And  the greater =   (x + 9)

Note that there is a difference of 18 units  between the integers

Note  that  their product is  ( x - 9) ( x + 9)  =  x^2  - 81

This is an upward turning parabola.....we will have no max.....but we will have a minimum  (at the vertex )

The  vertex  is at   (0, -81)....so  this is the  minimum  =  -81

Then this  must  imply  that  x  = 0       because  0^2   - 81   =   -81

So

( x - 9)  =  -9   ⇒  the lesser integer

And

(x + 9)  =   9 ⇒  the greater integer

Mar 27, 2020