lean_workbook_plus_42280

By Cauchy: $(a^2b^2+b^2c^2+c^2a^2)(b+c+a) \geq (ab\sqrt{b}+bc\sqrt{c}+ca\sqrt{a})^2$ So we want to prove $3 \geq (a^2b^2+b^2c^2+c^2a^2)$ Homogenizing: $(a+b+c)^4 \geq 27 (a^2b^2+b^2c^2+c^2a^2)$