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lp_qt

$A=2x^2+3y^2-4xy-8x-2y+18$

$=(\sqrt{2}.x)^2+(\sqrt{2}.y)^2+(2\sqrt{2})^2-2.\sqrt{2}x.\sqrt{2}y-2.\sqrt{2}x.2\sqrt{2}+2.\sqrt{2}y.2\sqrt{2}+y^2-10y+25-15$

$=(\sqrt{2}y+2\sqrt{2}-\sqrt{2}x)^2+(y-5)^2-15 \ge -15$

dấu = xảy ra\Leftrightarrow $\left\{\begin{matrix}y-5=0 & \\ \sqrt{2}y+2\sqrt{2}-\sqrt{2}x=0 & \end{matrix}\right.$
 
S

songdzianhem

lp_qt said:
$A=2x^2+3y^2-4xy-8x-2y+18$

$=(\sqrt{2}.x)^2+(\sqrt{2}.y)^2+(2\sqrt{2})^2-2.\sqrt{2}x.\sqrt{2}y-2.\sqrt{2}x.2\sqrt{2}+2.\sqrt{2}y.2\sqrt{2}+y^2-10y+25-15$

$=(\sqrt{2}y+2\sqrt{2}-\sqrt{2}x)^2+(y-5)^2-15 \ge -15$

dấu = xảy ra\Leftrightarrow $\left\{\begin{matrix}y-5=0 & \\ \sqrt{2}y+2\sqrt{2}-\sqrt{2}x=0 & \end{matrix}\right.$
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Đề là $A=2x^2+3y^2+4xy-8x-2y+18$ mà bạn
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