Proving Inequalities with Positive Real Numbers

[Sergio_Ontari]

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

 

[Char. Limit]

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.