Đáp án:
A=-2x²-20y²+8xy+4x+4y+2016
=-x²+4x-4-4y²+4y-1-x²+8xy-16y²+2011
=-(x²-4x+4)-(4y²-4y+1)-(x²-8xy+16y²)+2011
=-(x-2)²-(2y-1)²-(x-4y)²+2011
Vì -(x-2)²≤0
-(2y-1)²≤0
-(x-4y)²≤0
⇒-(x-2)²-(2y-1)²-(x-4y)²≤0
⇒-(x-2)²-(2y-1)²-(x-4y)²+2011≤2011
Dấu ''='' xảy ra⇔-(x-2)²-(2y-1)²-(x-4y)²=0
(x-2)²=0⇒x-2=0⇒x=2
⇒và (2y-1)²=0⇒2y-1=0⇒y=1/2
(x-4y)²=0⇒x-4y=0⇒x=4y(thỏa mãn)
Vậy Max A=2011 ⇔ x=2 và y=1/2
-Chúc bn hk tốt-