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Biến đổi pt đầu:
\(2x^2-2xy-xy+y^2-\left(x-y\right)=0\Leftrightarrow2x\left(x-y\right)-y\left(x-y\right)-\left(x-y\right)=0\)\(\Leftrightarrow\left(x-y\right)\left(2x-y-1\right)=0\Rightarrow\left[{}\begin{matrix}x-y=0\\2x-y-1=0\end{matrix}\right.\)
Nếu x-y=0 hay x=y, thay vào pt sau:
\(2x^2-y^2=1\Leftrightarrow2x^2-x^2=1\Rightarrow\left[{}\begin{matrix}x=1;y=1\\x=-1;y=-1\end{matrix}\right.\)
Nếu \(2x-y-1=0\Leftrightarrow y=2x-1\) thay vào pt sau ta được:
\(2x^2-\left(2x-1\right)^2=1\Leftrightarrow-2x^2+4x-2=0\Rightarrow x=1;y=1\)
Vậy hệ đã cho có 2 cặp nghiệm: {x;y}={-1;-1} hoặc {x;y}={1;1}
\(2x^2-\left(3y-3\right)x+y^2-2y+1=0\)
\(\Delta=\left(3y-3\right)^2-8\left(y^2-1y+1\right)=\left(y-1\right)^2\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{3y-3+y-1}{4}\\x=\dfrac{3y-3-y+1}{4}\end{matrix}\right.\)
\(\Rightarrow...\)
\(\Leftrightarrow\left\{{}\begin{matrix}4x^2-6xy+2y^2=6\\x^2+2xy-2y^2=6\end{matrix}\right.\)
\(\Rightarrow3x^2-8xy+4y^2=0\)
\(\Rightarrow\left(3x-2y\right)\left(x-2y\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}y=\dfrac{3}{2}x\\y=\dfrac{1}{2}x\end{matrix}\right.\)
Thế vào pt đầu...
\(\left\{{}\begin{matrix}2x^2-3xy+y^2=3\\x^2+2xy-2y^2=6\end{matrix}\right.\)\(\left(1\right)\)\(\Leftrightarrow\left\{{}\begin{matrix}4x^2-6xy+2y^2=6\\x^2+2xy-2y^2=6\end{matrix}\right.\)
\(\Leftrightarrow3x^2-8xy+4y^2=0\)
\(\Leftrightarrow3x\left(x-2y\right)-2y\left(x-2y\right)=0\)
\(\Leftrightarrow\left(x-2y\right)\left(3x-2y\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2y\\x=\dfrac{2y}{3}\end{matrix}\right.\)
Thay vào \(\left(1\right)\) ta được:
\(\Leftrightarrow\left[{}\begin{matrix}2.\left(2y\right)^2-3.2y.y+y^2=3\\2.\left(\dfrac{2y}{3}\right)^2-3.\dfrac{2y}{3}.y+y^2=3\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}y^2=1\\y^2=-27\left(VLý\right)\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}y=1\\y=-1\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x=2\\y=1\end{matrix}\right.\\\left\{{}\begin{matrix}x=-2\\y=-1\end{matrix}\right.\end{matrix}\right.\)
Vậy ...
\(1,\Leftrightarrow\left\{{}\begin{matrix}x=y+5\\2y+10+y=11\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{16}{3}\\y=\dfrac{1}{3}\end{matrix}\right.\\ 2,\Leftrightarrow\left\{{}\begin{matrix}3x=1-2y\\1-2y+y=2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=-1\end{matrix}\right.\\ 3,\Leftrightarrow\left\{{}\begin{matrix}x=y+2\\3y+6+2y=11\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=3\\y=1\end{matrix}\right.\)
1. \(\left\{{}\begin{matrix}3x+4y=11\\2x-y=-11\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}3x+4y=11\\8x-4y=-44\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}3x+4y=11\\11x=-33\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=5\\x=-3\end{matrix}\right.\)
2. \(\left\{{}\begin{matrix}3x+2y=0\\2x+y=-1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}3x+2y=0\\4x+2y=-2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=3\\x=-2\end{matrix}\right.\)
3.\(\left\{{}\begin{matrix}3x+\dfrac{5}{2}y=9\\2x+\dfrac{1}{3}y=2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}6x+5y=18\\6x+y=6\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}4y=12\\6x+y=6\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=3\\x=\dfrac{1}{2}\end{matrix}\right.\)
a) Ta có: \(\left\{{}\begin{matrix}3x-2\left|y\right|=9\\2x+3\left|y\right|=1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}6x-4\left|y\right|=18\\6x+9\left|y\right|=3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}-13\left|y\right|=15\\3x-2\left|y\right|=9\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left|y\right|=\dfrac{-15}{13}\\3x-2\left|y\right|=9\end{matrix}\right.\Leftrightarrow\)Phương trình vô nghiệmVậy: \(S=\varnothing\)
$\begin{cases}3x-2|y|=9\\2x+3|y|=1\\\end{cases}$
`<=>` $\begin{cases}6x-4|y|=18\\6x+9|y|=3\\\end{cases}$
`<=>` $\begin{cases}13|y|=-15(loại)\\|3x|-2|y|=9\\\end{cases}$
Vậy HPT vô nghiệm
Lời giải:
Lấy PT(1) cộng PT(2) thu được:
\(2x^3-x^2-2xy-3xy^2-y^2-y^3-1=0\)
\(\Leftrightarrow (2x^3-3xy^2-y^3)-(x^2+2xy+y^2)-1=0\)
\(\Leftrightarrow [2x^2(x+y)-2xy(x+y)-y^2(x+y)]-(x+y)^2-1=0\)
\(\Leftrightarrow (2x^2-2xy-y^2)(x+y)-(x+y)^2-1=0\)
\(\Leftrightarrow 2(x+y)-(x+y)^2-1=0\)
\(\Leftrightarrow -(x+y-1)^2=0\Rightarrow x+y=1\Rightarrow y=1-x\)
Thay vào PT(1) ta có:
\(2x^2-2x(1-x)-(1-x)^2=2\)
\(\Leftrightarrow 3x^2-3=0\Rightarrow x=\pm 1\)
\(x=1\Rightarrow y=0; x=-1\Rightarrow y=2\) (thỏa mãn)
Vậy $(x,y)=(1,0); (-1,2)$
Bạn ơi ! Đề bài đâu ạ ! Có mỗi chữ giải hệ phương trình à !
ko có đề bài à