4xy-x=y=5
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Ta có:
\(x^2+5y^2-4x-4xy+6y+5=0\\\Rightarrow[(x^2-4xy+4y^2)-(4x-8y)+4]+(y^2-2y+1)=0\\\Rightarrow[(x-2y)^2-4(x-2y)+4]+(y-1)^2=0\\\Rightarrow(x-2y-2)^2+(y-1)^2=0\)
Ta thấy: \(\left\{{}\begin{matrix}\left(x-2y-2\right)^2\ge0\forall x,y\\\left(y-1\right)^2\ge0\forall y\end{matrix}\right.\)
\(\Rightarrow\left(x-2y-2\right)^2+\left(y-1\right)^2\ge0\forall x,y\)
Mà: \(\left(x-2y-2\right)^2+\left(y-1\right)^2=0\)
nên: \(\left\{{}\begin{matrix}x-2y-2=0\\y-1=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=2y+2\\y=1\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=2\cdot1+2=4\\y=1\end{matrix}\right.\)
Thay \(x=4;y=1\) vào \(P\), ta được:
\(P=\left(4-3\right)^{2023}+\left(1-2\right)^{2023}+\left(4+1-5\right)^{2023}\)
\(=1^{2023}+\left(-1\right)^{2023}+0^{2023}\)
\(=1-1=0\)
Vậy \(P=0\) khi \(x=4;y=1\).
Câu 2:
\(B=x^2+2x+y^2-2x-2xy+37\)
\(=\left(x^2-2xy+y^2\right)+2\left(x-y\right)+37\)
\(=\left(x-y\right)^2+2\left(x-y\right)+37\)
\(=7^2+2\cdot7+37=49+37+14=100\)
Câu 3:
\(C=\left(x^2+4xy+4y^2\right)-2\left(x+2y\right)+10\)
\(=\left(x+2y\right)^2-2\left(x+2y\right)+10\)
\(=5^2-2\cdot5+10=25\)
\(x^3+y^3-2x^2-2y^2+3xy\left(x+y\right)-4xy+3\left(x+y\right)+10=\left[x^3+y^3+3xy\left(x+y\right)\right]-2\left(x^2+2xy+y^2\right)+3\left(x+y\right)+10=\left(x+y\right)^3-2\left(x+y\right)^2+3\left(x+y\right)+10=5^3-2.5^2+3.5+10=100\)
b) \(2x^2+4y^2+z^2-4xy-2x-2z+5=0\)
\(\Leftrightarrow\left(x^2-4xy+4y^2\right)+\left(x^2-2x+1\right)+\left(z^2-2z+1\right)+3=0\)
....
a) \(x^2+5y^2-4xy+6y+9=0\)
\(\Leftrightarrow\left(x^2-4xy+4y^2\right)+\left(y^2+6y+9\right)=0\)
\(\Leftrightarrow\left(x-2y\right)^2+\left(y+3\right)^2=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}x-2y=0\\y+3=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=2y=2.\left(-3\right)=-6\\y=-3\end{matrix}\right.\)
Vậy : \(\left(x,y\right)=\left(-6,-3\right)\)
\(A=x\left(2x+1\right)-4xy+y\left(2y-1\right)+2000.\)
\(2x^2+x-4xy+2y^2-y+2000\)
\(2\left(x-y\right)^2+x-y+2000=2.25+5+2000\)
danh nham 4xy-x+y=5
=> y = 5
xét 4xy vì y = 5
=> 4xy >= 20 ( >= lớn hơn hoạc bằng )
mà 4xy - x =5 => x ko có giá trị