Is my solution for this inequality correct?

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Lizu
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Hi! I would like to know if my solution for this inequality is corect or not:
Handwritten proof on paper: show that (a^4+b^4)/(a^2+b^2) + (b^4+c^4)/(b^2+c^2) + (c^4+a^4)/(c^2+a^2) >= ab+bc+ca for a,b,c>0, using the Cauchy-Bunyakovski-Schwarz inequality, with a chain of inequalities ending in a^2+b^2+c^2 >= ab+bc+ca.
 
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