[Toán 8] tìm GTNN của biểu thức: $A=2x^2+2xy+5y^2-8x-22y$

N

nguyenbahiep1

[TEX]2.x^2 + 2.x(y-4) + 5.y^2 -22y \\ 2.( x + \frac{y+4}{2})^2 + \frac{10y^2 -44y - (y+4)^2}{2} \\ 2.( x + \frac{y+4}{2})^2 + \frac{9y^2 -52y -16}{2} \\ 2.( x + \frac{y+4}{2})^2 + \frac{9(y -\frac{26}{9})^2 - \frac{820}{9}}{2} \\ 2.( x + \frac{y+4}{2})^2 + \frac{9}{2}.(y -\frac{26}{9})^2 - \frac{410}{9} \geq - \frac{410}{9} \\ \Rightarrow min A = - \frac{410}{9} \\ y = \frac{26}{9} \\ x= -\frac{31}{9}[/TEX]
 
You must log in or register to reply here.
Top Bottom