I actually i tried a lot of inequalities (Cauchy-Schwarz etc), but nothing came up with this demostration, Im stuck here, its a difficult solution or Im just dump??
Welcome to SE. As you are asking on a side for math educators, I assume that you want to explain this to students. My advice: don't. Start with much, much easier examples to get the students accustomed to such problems, then come back to it later; if at all.
If you, as the teacher/professor, are not able to find a solution for this problem, it is too hard for students who are new to the topic.
Furthermore, you have to really understand all the concepts behind it. Therefore, reciting an answer you might get here on how to do it might not be convincing and thus bad for your students.
In case that this is a homework problem or you are looking for how to answer it for different reasons than teaching it, you might want to try at Math.SE.