## Inequality – \$ 2 left[(mz)^2 + (px)^2 + pmy^2right] + left[(nz)^2 + (nx)^2 + (py)^2 + (my)^2right] ge 2 (2pmzx + pnzy + mnxy + pnxy + mnzy) \$

$$x, y, z$$ Y $$m, n, p$$ are real Try / disprove that $$2 large left[(mz)^2 + (px)^2 + pmy^2right] + left[(nz)^2 + (nx)^2 + (py)^2 + (my)^2right] ge 2 (2pmzx + pnzy + mnxy + pnxy + mnzy)$$

That is the problem and I do not know how to do it.

My original idea is to convert the difference between the left and right sides into a sum of squares and then use the Cauchy-Schwarz inequality (it was not accredited to Bunyakovsky) but it was not successful.