perplexus.info :: Just Math : Is It Necessary and Sufficient

Is It Necessary and Sufficient (Posted on 2008-02-27)

Let a,b,c be real numbers. Is a,b,c≥0 the necessary and sufficient condition to show that a³+b³+c³≥3abc? If not, find the condition that is both sufficient and necessary.

Submitted by Praneeth

Rating: 3.5000 (2 votes)

Solution: (Hide)

The necessary and sufficient condition: (a+b+c)≥0 or a=b=c.
Explanation:
Look at K Sengupta's Solution
Thanks to K Sengupta for solution and Steve Herman for the correction.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
re: Puzzle Solution -- minor correction	K Sengupta	2008-02-28 05:05:19
Puzzle Solution -- minor correction	Steve Herman	2008-02-28 01:29:45
Puzzle Solution	K Sengupta	2008-02-27 23:57:58
More thoughts; Solution?	Steve Herman	2008-02-27 23:45:35
Stating the obvious ...	Steve Herman	2008-02-27 11:34:08

Please log in:

Login:
Password:
Remember me:

Sign up! \| Forgot password

Search:

Search body:

Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (8)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info