lean_workbook_plus_18095

Prove that for real numbers $x, y, z$,\n$a. (x^2z^2 + x^2y^2 + y^2z^2)^2 \geq 3(x^2 + y^2 + z^2)x^2y^2z^2$\n$b. (x^4 + y^4 + z^4)(x^2z^2 + x^2y^2 + y^2z^2) \geq (xy^3 + yz^3 + x^3z)^2$\n$c. (x^2 + y^2 + z^2)^4 \geq \frac{9}{2}(y^3x + z^3y + x^3z)^2 + \frac{9}{2}(z^3x + x^3y + y^3z)^2$