lean_workbook_plus_68905

$WLOG$ , assume that $a \geq b \geq c > 0$ . Then we have : \n\n $i)$ $\frac{a^2}{b^2+c^2} \geq \frac{b^2}{c^2+a^2} \geq \frac{c^2}{a^2+b^2}$ \n\n $ii)$ $\frac{b+c}{2a+b+c} \leq \frac{c+a}{2b+c+a} \leq \frac{a+b}{2c+a+b}$