Help to prove the following

  • #1
1. c, d positive real numbers and c+d=1 prove that (c+1/c)2+(d+1/d)2>=25/2



2. Prove the previous also formulate and prove a generalization for n



3. I first tried to expand but got stuck, I thought of using Binomial but also got stuck. I tried to do (a+b)2 were a=(c+1/c) and b=(d+1/d) but also nothing
Any help is appreciated
 
Last edited:

Answers and Replies

  • #2
Char. Limit
Gold Member
1,208
14
Well, if c is greater than d, and c=1-d, then 1-d > d. Add d to both sides and divide by 2 to get that .5>d. So you know that .5>d, and similar processes lead you to the fact that c>.5 . I have a feeling that this might help you, but I'm not sure.
 

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