Gtnn

B

braga

[TEX]S=x^2+xy+y^2-3x-3y+2000[/TEX]

[TEX]=(x-1)^2+(y-1)^2+xy-x-y+1998 \\ =(x-1)^2+(y-1)^2+x(y-1)-(y-1)+1997 \\ =(x-1)^2+(y-1)^2+(y-1)(x-1)+1997 \\ =\left [ (x-1)+\frac{y-1}{2} \right ]^2+\frac{3}{4}(y-1)^2+1997\geq 1997[/TEX]

Dấu "=" xảy ra [TEX]\Leftrightarrow x=y=1[/TEX]

Vậy [TEX]MinS=1997 \Leftrightarrow x=y=1[/TEX]
 
Last edited by a moderator:
You must log in or register to reply here.
Top Bottom