Please check my proof

[shivers20]

1. Let a,b,c and d be non-negative real numbers. Prove:
((a+b+c+d)/4) >= 4sqrt[abcd]

[Hint: Focus on the left side of the inequality. Rewrite it in such a way that you can use AM-GM inequality theorem. Then use AM-GM again.]

2. Let a,b,c be non-negative real numbers. Prove:
((a+b+c)/3) >= 3sqrt[abc]

[Hint: Use the inequality in part 1, with d=3sqrt[abc]

3. If a,b and c are positive numbers, show that a/b+ b/c+ c/a >= 3

 

[marcmtlca]

its good... only thing is the first inequality should not be strict and i would add the first line (sqrt(x)-sqrt(y))^2 >= 0 just to be clearer. but ya i dont see a mistake.

M