Tim Min

B

buithinhvan77

Tách đưa về các bình phương đúng cộng hằng số!

[tex]B =3x^2 - 6xy + 5y^2 - y + 3x + 2011 = [3(x^2 - 2xy + y^2) - 3( y - x) + \frac{3}{4}] + 2(y^2 + y + \frac{1}{4}) - \frac{3}{4} - \frac{2}{4} + 2011 [/tex]

[tex]B = 3[(y-x)^2 - 2.\frac{1}{2} (y - x) + \frac{1}{4}] + 2(y + \frac{1}{2})^2 - \frac{5}{4}+ 2011 [/tex]

[tex]B = 3(y - x - \frac{1}{2})^2 + 2(y + \frac{1}{2})^2 + \frac{8039}{4} \geq \frac{8039}{4} [/tex]

Vậy [tex]Min B = \frac{8039}{4} \Leftrightarrow x = -1; y = \frac{-1}{2}[/tex]
 
Last edited by a moderator:
You must log in or register to reply here.
Top Bottom