2x - 2y = 2016. tìm x, y
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2x2 + 2y2 -2xy+2x+2y+2=0
<=>x2-2xy+y2+x2+2x+1+y2+2y+1=0
<=>(x-y)2+(x+1)2+(y+1)2=0
<=>x=-1;y=-1
![](https://rs.olm.vn/images/avt/0.png?1311)
\(C=2\left(x-y\right)+13x^3y^2\left(x-y\right)-15xy\left(x-y\right)+1=1\)
Vậy C=1
\(C=2x-2y+13x^3y^2\left(x-y\right)+15\left(y^2x-x^2y\right)+\left(\dfrac{2015}{2016}\right)^0\)
\(C=2\left(x+y\right)+13x^3y^2\left(x-y\right)+15xy\left(x-y\right)+1\)
Mà x - y = 0 (bài cho)
\(\Rightarrow C=2.0+13x^3y^2.0+15xy.0+1\)
\(C=1\)
Vậy C=1
![](https://rs.olm.vn/images/avt/0.png?1311)
\(B=2x^2+2xy+y^2-2x+2y+2016\)
\(=\left(x^2+2xy+y^2+2x+2y+1\right)+\left(x^2-4x+4\right)+2011\)
\(=\left[\left(x+y\right)^2+2\left(x+y\right)+1\right]+\left(x-2\right)^2+2011\)
\(=\left(x+y+1\right)^2+\left(x-2\right)^2+2011\ge2011\forall x;y\)có GTNN là 2011
Dấu "=" xảy ra \(\Leftrightarrow\hept{\begin{cases}\left(x+y+1\right)^2=0\\\left(x-2\right)^2=0\end{cases}\Leftrightarrow\hept{\begin{cases}x=2\\y=-3\end{cases}}}\)
Vậy \(B_{min}=2011\) tại \(x=2;y=-3\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có:
\(C=2\left(x-y\right)+13x^3y^2\left(x-y\right)-15xy\left(x-y\right)+1\)
=\(0+0+0+1=1\)
\(C=2x-2y+13x^3y^2\left(x-y\right)+15\left(y^2x-x^2y\right)+\left(\dfrac{2015}{2016}\right)^0\)
\(=2\left(x-y\right)+13x^3y^2\left(x-y\right)-15xy\left(x-y\right)\)
\(=0+0+1=1\)
~^~
![](https://rs.olm.vn/images/avt/0.png?1311)
Theo bài ra , ta có :
\(2x^2+2y^2+2x+2y+2xy=0\)
\(\Rightarrow\left(x+y\right)^2+\left(x+1\right)^2+\left(y+1\right)^2=0\)
\(\Leftrightarrow\hept{\begin{cases}x+y=0\\x+1=0\\y+1=0\end{cases}\Leftrightarrow x=y=-1}\)
Thay x = y = -1 vào A ta được :
\(A=\left(x+2\right)^{2016}+\left(y+1\right)^{2017}\)
\(\Leftrightarrow A=\left(-1+2\right)^{2016}+\left(-1+1\right)^{2017}=1^{2016}+0=1\)
Vậy A=1
Chúc bạn học tốt =))
![](https://rs.olm.vn/images/avt/0.png?1311)
2x2 + 2y2 + 2x + 2y + 2xy = 0
<=> (x+y)2 + (x+1)2 +(y+1)2 = 0
<=> \(\left\{\begin{matrix}\left(x+y\right)^2=0\\\left(x+1\right)^2=0\\\left(y+1\right)^2=0\end{matrix}\right.\) <=> x = y = -1
thay x = y = -1 vào A ta được
(-1 + 2)2016 + (-1 + 1)2017 = 12016 = 1
chúc may mắn!!
![](https://rs.olm.vn/images/avt/0.png?1311)
=>(x+2y-3)^2016=0 hoặc |2x+3y-5|=0
x+2y=3 hoặc 2x+3y=5
<=>x=3-2y
Ta có 2x+3y=5=>6-4y+3y=5
6-y=5
y=1
Ta có x+2y=3=>x+2*1=3
x+2=3
x=1
Vậy (x;y) =(1;1)