Inequalities

Watch this thread
esrever
Badges: 20
Rep:
? You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#1
Report Thread starter 4 years ago
#1
Prove that \sum_{\text{cyc}} \frac{1}{a^3 + b^3 + abc} \leq \frac{1}{abc} for positive reals.

I was able to reduce the problem to \sum_{\text{cyc}} \frac{1}{x+y+1} \leq 1 where x = a^3 and so on. Not sure what to do now.
0
reply
ghostwalker
Badges: 17
? You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#2
Report 4 years ago
#2
(Original post by esrever)
Prove that \sum_{\text{cyc}} \frac{1}{a^3 + b^3 + abc} \leq \frac{1}{abc} for positive reals.

I was able to reduce the problem to \sum_{\text{cyc}} \frac{1}{x+y+1} \leq 1 where x = a^3 and so on. Not sure what to do now.
Can't comment on your original problem, but if I understand it correctly, the one you've reduced it to isn't true. E.g. let a=b=c=0.1, then LHS = 3/1.002 which is greater than 1. Post your working so far, if you'd like someone to check it.
0
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Back
to top
Latest

Does school Maths prepare people well enough for the future?

Yes, it gives everyone a good foundation for any future path (23)
33.33%
Somewhat, if your future involves maths/STEM (31)
44.93%
No, it doesn't teach enough practical life skills (14)
20.29%
Something else (tell us in the thread) (1)
1.45%

Watched Threads

View All