\(\Leftrightarrow\left(x^2+y^2\right)\left(x+y\right)+2xy=x+y\)
\(\Leftrightarrow\left(x^2+y^2\right)\left(x+y\right)+\left(x+y\right)^2-\left(x^2+y^2\right)=x+y\)
\(\Leftrightarrow\left(x^2+y^2\right)\left(x+y-1\right)+\left(x+y\right)\left(x+y-1\right)=0\)
\(\Leftrightarrow\left(x^2+y^2+x+y\right)\left(x+y-1\right)=0\)
giải hệ phương trình
1 , \(\left\{{}\begin{matrix}\left(x+y\right)\left(x-1\right)=\left(x-y\right)\left(x+1\right)+2xy\\\left(y-x\right)\left(y-1\right)=\left(y+x\right)\left(y-2\right)-2xy\end{matrix}\right.\)
2, \(\left\{{}\begin{matrix}2\left(\frac{1}{x}+\frac{1}{2y}\right)+3\left(\frac{1}{x}-\frac{1}{2y}\right)^2=9\\\left(\frac{1}{x}+\frac{1}{2y}\right)-6\left(\frac{1}{x}-\frac{1}{2y}\right)^2=-3\end{matrix}\right.\)
3 , \(\left\{{}\begin{matrix}\frac{xy}{x+y}=\frac{2}{3}\\\frac{yz}{y+z}=\frac{6}{5}\\\frac{zx}{z+x}=\frac{3}{4}\end{matrix}\right.\)
4 , \(\left\{{}\begin{matrix}2xy-3\frac{x}{y}=15\\xy+\frac{x}{y}=15\end{matrix}\right.\)
5 , \(\left\{{}\begin{matrix}x+y+3xy=5\\x^2+y^2=1\end{matrix}\right.\)
6 , \(\left\{{}\begin{matrix}x+y+xy=11\\x^2+y^2+3\left(x+y\right)=28\end{matrix}\right.\)
7, \(\left\{{}\begin{matrix}x+y+\frac{1}{x}+\frac{1}{y}=4\\x^2+y^2+\frac{1}{x^2}+\frac{1}{y^2}=4\end{matrix}\right.\)
8, \(\left\{{}\begin{matrix}x+y+xy=11\\xy\left(x+y\right)=30\end{matrix}\right.\)
9 , \(\left\{{}\begin{matrix}x^5+y^5=1\\x^9+y^9=x^4+y^4\end{matrix}\right.\)
\(\left\{{}\begin{matrix}x+\frac{2xy}{\sqrt[3]{x^2-2x+9y}}=x^2+y\\y+\frac{2xy}{\sqrt[3]{y^2-2y+9}}=y^2+x\end{matrix}\right.\)
\(\left\{{}\begin{matrix}2xy=x+y+1\\\frac{x^2}{\left(y+1\right)^2}+\frac{y^2}{\left(x+1\right)^2}=\frac{10}{9}\end{matrix}\right.\)
Tìm cặp số nguyên x,y thỏa mãn pt:
2015(x^2+y^2)-2014(2xy+1)=25
Giải hệ pt
a) \(\left\{{}\begin{matrix}x^2+2xy^2=3\\y^3+y+x\left(2xy-1\right)=3\end{matrix}\right.\)
b) \(\left\{{}\begin{matrix}x^2+x^3y-xy^2+xy-y=1\\x^4+y^2-xy\left(2x-1\right)=1\end{matrix}\right.\)
giải hẹ phương trình: \(\left\{{}\begin{matrix}\sqrt{2x+y}+x=\frac{3-y}{2}\\x^2-2xy-y^2=2\end{matrix}\right.\)
Giải giúp 2 bài sau nha mọi người
Thanks nhìu
1. Giải hệ pt: \(\left\{{}\begin{matrix}x^2+2xy-2x-y=0\\x^4-4\left(x+y-1\right)x^2+y^2+2xy=0\end{matrix}\right.\)
2. Tìm x, y thuộc Z sao cho \(x^4-x^3+1=y^2\)
Tìm tham số m để hệ phương trình sau có nghiệm thực:
\(\begin{cases}X\sqrt{Y}+Y\sqrt{X}+2\left(\sqrt{X}+\sqrt{Y}\right)=12\sqrt{XY}\\X+2\sqrt{Y}+4\left(\frac{1}{X}+\frac{1}{\sqrt{Y}}\right)=m\left(\frac{X+2}{\sqrt{X}}\right)\end{cases}\)
\(\left\{{}\begin{matrix}x-y+\frac{2y}{x}=-2\\2xy-2y^2+x=0\end{matrix}\right.\)
