lean_workbook_plus_57996

Now, we will prove that\n\n$9x^{2}+25y^{2}+225z^{2}\ge 15(xy+3xz+5yz)$\n\n$\implies 2\left(9x^{2}+25y^{2}+225z^{2}\right)\ge 30(xy+3xz+5yz)$\n\n$\implies \left(9x^2-30xy+25y^2\right)+\left(25y^2-150yz+225z^2\right)+\left(225z^2-90zx+9x^2\right)\ge 0$\n\n$\implies (3x-5y)^2+(5y-15z)^2+(15z-3x)^2\ge 0$