P = x^2 + xy + y^2 - 3x - 3y + 2010
= x^2 + x(y - 3) + y^2 - 3y + 2010
= x^2 + 2.x(y - 3)/2 + (y - 3)^2/4 + [(y^2 - 3y)4 - (y - 3)^2]/4 + 2010
= [x + (y - 3)/2]^2 + (4y^2 - 12y - y^2 + 6y - 9)/4 + 2010
= [x + (y - 3)/2]^2 + [(3y^2 - 6y + 3 )- 12]/4 + 2010
= [x + (y - 3)/2]^2 + 3(y - 1)^2/4 - 12/4 + 2010
= [x + (y - 3)/2]^2 + 3(y - 1)^2/4 + 2007
[x + (y - 3)/2]^2 + 3(y - 1)^2/4 >= 0
=> P >= 2007 .
=> P nhỏ nhất = 2007 <=> [x + (y - 3)/2]^2 + 3(y - 1)^2/4 = 0
<=> x = y = 1 .
Vậy P min = 2007 khi và chỉ khi x = y = 1 .
hơi P=x^2+xy+y^2-3x-3y+2010