Tìm x X^2-2x-1=0 Tìm GTNN của biểu thức A=3x^2+2x+1 B=10x^2+4y^2-4xy+12x-30

$$\eqalign{ & {x^2} - 2x - 1 = 0 \cr & \Delta ' = 1 + 1 = 2 > 0 \cr & \Rightarrow PT\,\,co\,\,2\,\,nghiem\,\,pb \cr & \Rightarrow \left[ \matrix{ {x_1} = 1 + \sqrt 2 \hfill \cr {x_2} = 1 - \sqrt 2 \hfill \cr} \right. \cr & \cr & A = 3{x^2} + 2x + 1 \cr & A = 3\left( {{x^2} + {2 \over 3}x} \right) + 1 \cr & A = 3\left( {{x^2} + 2x.{1 \over 3} + {1 \over 9}} \right) - {1 \over 3} + 1 \cr & A = 3{\left( {x + {1 \over 3}} \right)^2} + {2 \over 3} \cr & 3{\left( {x + {1 \over 3}} \right)^2} \ge 0 \Rightarrow 3{\left( {x + {1 \over 3}} \right)^2} + {2 \over 3} \ge {2 \over 3} \cr & \Rightarrow A \ge {2 \over 3} \Rightarrow \min A = {2 \over 3} \cr & B = 10{x^2} + 4{y^2} - 4xy + 12x - 30 \cr & B = 9{x^2} + 12x + 4 + {x^2} - 4xy + 4{y^2} - 34 \cr & B = {\left( {3x + 2} \right)^2} + {\left( {x - 2y} \right)^2} - 34 \cr & \Rightarrow B \ge - 34 \cr & \Rightarrow \min B = - 34 \Leftrightarrow \left\{ \matrix{ 3x + 2 = 0 \hfill \cr x - 2y = 0 \hfill \cr} \right. \Leftrightarrow \left\{ \matrix{ x = - {2 \over 3} \hfill \cr y = - {1 \over 3} \hfill \cr} \right. \cr} $$