Need help with an inequality.

  • Thread starter pixel01
  • Start date
  • #1
688
0
Can anyone help me to prove this inequality:

(a^2)/b+(b^2)/c+(c^2)/a >= a+b+c.

I know i must use Cauchy formula, but can not prove it.

Thank you .
 

Answers and Replies

  • #2
malawi_glenn
Science Advisor
Homework Helper
4,786
22
What do you mean, that you dont know how to prove cauchy's inequality? Or that you can not come to that point where you have the equation on the form of cauchy's inequality?
 
  • #3
688
0
Thank you. I've solved it myself. This is one of the homework series that i have to use cauchy's inequality.

Can you help me to prove this one:

a/(a+b)+b/(b+c)+c/(c+a) > sqrt(a/(b+c)) + sqrt(b/(a+c)) + sqrt(c/(a+b)).
 
  • #4
malawi_glenn
Science Advisor
Homework Helper
4,786
22
Thank you. I've solved it myself. This is one of the homework series that i have to use cauchy's inequality.

Can you help me to prove this one:

a/(a+b)+b/(b+c)+c/(c+a) > sqrt(a/(b+c)) + sqrt(b/(a+c)) + sqrt(c/(a+b)).

what have you done so far?..
 
  • #5
688
0
My idea by now is :
a/(a+b)<1, b/(b+c)< 1 and c/(c+a)<1, so the left hand side is smaller than sqrt(a/(a+b))+sqrt(b/(b+c))+sqrt(c/(c+a)).
Then I try to compare the right hand side with sqrt(a/(a+b))+sqrt(b/(b+c))+sqrt(c/(c+a)) because they are both in the square root type (i hope it will be easier). But it doesn't work so far. Can you give me some hints.
 

Related Threads on Need help with an inequality.

  • Last Post
Replies
16
Views
1K
  • Last Post
Replies
2
Views
2K
Replies
11
Views
2K
Replies
30
Views
3K
  • Last Post
Replies
9
Views
2K
Replies
4
Views
1K
  • Last Post
Replies
6
Views
2K
Q
Replies
2
Views
2K
Replies
2
Views
694
  • Last Post
Replies
5
Views
1K
Top