lean_workbook_plus_14459

By Cauchy-Schwarz \n $\sum_{cyc}{\frac{a}{2a+b+c}}\sum_{cyc}{\frac{a^2}{2ab+bc+ca}}\geq\frac{(a+b+c)^2}{\sum\limits_{cyc}(2a^2+2ab)}\cdot\frac{(a+b+c)^2}{4(ab+ac+bc)}\geq\frac{9}{16}$ , \n where the last inequality is equivalent to $\sum_{cyc}(2a^4-a^3b-a^3c+3a^2b^2-3a^2bc)\geq0$ , which is obvious.