Help to prove the following

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

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