lean_workbook_plus_39996

we just need to prove \n\n $\frac {(\sum \frac {1}{x^2})^2}{\sqrt {3\sum x^2(x^2 + 2y^2)}}\geq \frac {{\sqrt 3 }}{{{x^2}{y^2}{z^2}}}$ $\Longleftrightarrow \sum_{cyc} (x^4y^4 - x^4y^2z^2)\geq 0 \Longleftrightarrow$ $\frac {1}{2}\sum_{sym} (x^4y^4 - x^4y^2z^2)\geq 0$