lean_workbook_plus_30361

Cauchy-Schwarz: $(a^7+b^7+c)(\frac{1}{a^3}+\frac{1}{b^3}+c^3) \ge (a^2+b^2+c^2)^2$ so $\frac{1}{a^7+b^7+c} \le \frac{b^3c^3+a^3c^3+c^3}{(a^2+b^2+c^2)^2}$ . Then, the problem would reduce to $\sum_{cyc} c^3(a+b)(a^3+b^3+1) \le 2(a^2+b^2+c^2)^2$.