Markos Andres

prove that $$\sum_{cyc}\frac{a^2}{b} +\frac{3n}{a^2+b^2+c^2}\ge 3+n$$ where $a,b,c>0$ and $n\ge0,n\le 3$,$a+b+c=ab+bc+ca$ My try: by given condition $a+b+c=ab+bc+ca$ we have $a+b+c\le a^2+b^2+c^2$ also using titu's lemma $$\sum_{cyc}\frac{a^2}{b} +\frac{3n}{a^2+b^2+c^2}\ge a+b+c +\frac{3n}{a^2+b^...