lean_workbook_plus_22365

From Moldova TST $2005$ : $a^3b^2+b^3c^2+c^3a^2\ge abc(a^2+b^2+c^2)$ and IMO $1983$ : $a^3b+b^3c+c^3a \ge a^2b^2+b^2c^2+c^2a^2$ we also have a nice inequality: \n\n $\frac{a^3(a+b)}{a^2+b^2}+\frac{b^3(b+c)}{b^2+c^2}+\frac{c^3(c+a)}{c^2+a^2} \ge a^2+b^2+c^2$ .