$\begin{array}{l} A = x\left( {x + 1} \right)\left( {x - 2} \right)\left( {x - 3} \right)\\ A = x\left( {x - 2} \right)\left( {x + 1} \right)\left( {x - 3} \right)\\ A = \left( {{x^2} - 2x} \right)\left( {{x^2} - 2x - 3} \right)\\ A = {\left( {{x^2} - 2x} \right)^2} - 3\left( {{x^2} - 2x} \right)\\ A = {\left( {{x^2} - 2x} \right)^2} - 3\left( {{x^2} - 2x} \right) + \dfrac{9}{4} - \dfrac{9}{4}\\ A = {\left( {{x^2} - 2x - \dfrac{3}{2}} \right)^2} - \dfrac{9}{4} \ge - \dfrac{9}{4}\\ \Rightarrow \min A = - \dfrac{9}{4} \Leftrightarrow {x^2} - 2x - \dfrac{3}{2} = 0\\ \Leftrightarrow x = \dfrac{{2 \pm \sqrt {10} }}{2}\\ CMR:3\left( {{x^2} + {y^2} + {z^2}} \right) \ge {\left( {x + y + z} \right)^2}\\ \Leftrightarrow 3{x^2} + 3{y^2} + 3{z^2} \ge {x^2} + {y^2} + {z^2} + 2xy + 2yz + 2zx\\ \Leftrightarrow 2{x^2} - 2xy + 2{y^2} - 2yz + 2{z^2} - 2xz \ge 0\\ \Leftrightarrow {\left( {x - y} \right)^2} + {\left( {y - z} \right)^2} + {\left( {z - x} \right)^2} \ge 0\\ \Rightarrow BDT\,luon\,dung\\ B = {x^2} + {y^2} + {z^2} \ge \dfrac{{{{\left( {x + y + z} \right)}^2}}}{3} = \dfrac{1}{3}\\ \Rightarrow \min B = \dfrac{1}{3} \Rightarrow \left\{ \begin{array}{l} x + y + z = 1\\ x = y = z \end{array} \right. \Rightarrow x = y = z = \dfrac{1}{3} \end{array}$
