The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.math

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Try and find a geometrical proof for this one, George. (Or, anyone else!)
Replies: 10   Last Post: Mar 19, 2014 9:09 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]

Posts: 918
Registered: 12/15/13
Try and find a geometrical proof for this one, George. (Or, anyone else!)
Posted: Mar 17, 2014 9:07 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

At MID <532668f0$0$504$>, George Cornelius very
quickly and elegantly found, via wholly geometric means, the minimum value
of (x+y)(x+z) where xyz(x+y+z)=1 and x,y,z>0 [all negative would also work].

So, try to find a geometric solution to this one, then... I cannot.

x, y, z > 0
1/3 <= xy + yz + zx <= 3
What are the highest and lowest possible values of each of:
(a) xyz
(b) x + y + z ?

Failing a geometric solution (which I frankly doubt exists, except perhaps
in a very artificial / contrived manner), let's see if an elegant "other"
method can be found.

Again, calculus is prohibited.

Intuition may get one to the answer quickly, but a rigorous proof is needed.

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.