\(x^3+3x^2+4x+2=8y^3+2y\)
\(\Leftrightarrow\left(x+1\right)^3-\left(2y\right)^3+\left(x+1-2y\right)=0\)
\(\Leftrightarrow\left(x+1-2y\right)\left[\left(x+1\right)^2+2y\left(x+1\right)+4y^2+1\right]=0\)
\(\Leftrightarrow x+1-2y=0\Rightarrow2y=x+1\)
\(\Rightarrow x^3-x\left(x+1\right)-\frac{1}{3}=0\)
\(\Leftrightarrow3x^3-3x^2-3x-1=0\)
\(\Rightarrow x=\frac{\sqrt[3]{16}+\sqrt[3]{4}+1}{3}\)
giải hệ phương trình:
1, \(\left\{{}\begin{matrix}\left(x+y-3\right)^3=4y^3\left(x^2y^2+xy+\frac{45}{4}\right)\\x+4y-3=2xy^2\end{matrix}\right.\)
2, \(\left\{{}\begin{matrix}x^3+7y=\left(x+y\right)^2+x^2y+7x+4\\3x^2+y^2+8y+4=8x\end{matrix}\right.\)
3, \(\left\{{}\begin{matrix}2x+5y=xy+2\\x^2+4y+21=y^2+10x\end{matrix}\right.\)
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 , \(\left\{{}\begin{matrix}x^5+y^5=1\\x^9+y^9=x^4+y^4\end{matrix}\right.\)
Giải hệ pt
a) \(\left\{{}\begin{matrix}x^2+8y^2=12\\x^3+2xy^2+12y=0\end{matrix}\right.\)
b) \(\left\{{}\begin{matrix}x^3+y^3=1\\x^7+y^7=\left(x^4+y^4\right).1\end{matrix}\right.\)
giải hệ phương trình
\(\left\{{}\begin{matrix}\left(x+3y+1\right)\sqrt{2xy+2y}=y\left(3x+4y+3\right)\\\left(\sqrt{x-3}-\sqrt{2y-2}\right)\left(x-3+\sqrt{x^2+x+2y-4}\right)=4\end{matrix}\right.\)
Giải hệ
\(\left\{{}\begin{matrix}x^3+7y=\left(x+y\right)^2+x^2y+7x+4\\3x^2+y^2+8y+4=8x\end{matrix}\right.\)
giải hệ phương trình:
1, \(\left\{{}\begin{matrix}x^3+2y^2=x^2y+2xy\\2\sqrt{x^2-2y-1}+\sqrt[3]{y^3-14}=x-2\end{matrix}\right.\)
2, \(\left\{{}\begin{matrix}2\sqrt{x+y^2+y+3}-3\sqrt{y}=\sqrt{x+2}\\y^3+y^2-3y-5=3x-3\sqrt[3]{x}+2\end{matrix}\right.\)
3, \(\left\{{}\begin{matrix}\left(x-2\right)\left(2y-1\right)=x^3+20y-28\\2\left(\sqrt{x+2y}+y\right)=x^2+x\end{matrix}\right.\)
hệ phương trình
1 ,\(\left\{{}\begin{matrix}\frac{2x-3}{2y-5}=\frac{3x+1}{3y-4}\\2\left(x-3\right)-3\left(y+2\right)=-16\end{matrix}\right.\)
2, \(\left\{{}\begin{matrix}\frac{x}{y}=\frac{3}{2}\\3x-2y=5\end{matrix}\right.\)
3, \(\left\{{}\begin{matrix}\frac{x^2-y-6}{x}=x-2\\x+3y=8\end{matrix}\right.\)
4, \(\left\{{}\begin{matrix}\frac{x}{y}=\frac{2}{3}\\x+y=10\end{matrix}\right.\)
5, \(\left\{{}\begin{matrix}\frac{y^2+2x-8}{y}=y-3\\x+y=10\end{matrix}\right.\)
6 , \(\left\{{}\begin{matrix}\frac{x+1}{y-1}=5\\3\left(2x-2\right)-4\left(3x+4\right)=5\end{matrix}\right.\)
7, \(\left\{{}\begin{matrix}2x+y=4\\\left|x-2y\right|=3\end{matrix}\right.\)
8 , \(\left\{{}\begin{matrix}\frac{2x}{x+1}+\frac{y}{y+1}=3\\\frac{x}{x+1}-\frac{3y}{y+1}=-1\end{matrix}\right.\)
9 , \(\left\{{}\begin{matrix}y-\left|x\right|=1\\2x-y=1\end{matrix}\right.\)
10 , \(\left\{{}\begin{matrix}\sqrt{x+3y}=\sqrt{3x-1}\\5x-y=9\end{matrix}\right.\)
giải giúp mik bt này vs mn!
1)\(\left\{{}\begin{matrix}2x^2+y^2+x=3\left(xy+1\right)+2y\\\dfrac{2}{3+\sqrt{2x-y}}+\dfrac{2}{3+\sqrt{4-5x}}=\dfrac{9}{2x-y+9}\end{matrix}\right.\)
2)\(\left\{{}\begin{matrix}\left(x+3y+1\right)\sqrt{2xy+2y}=y\left(3x+4y+3\right)\\\left(\sqrt{x+3}-\sqrt{2y-2}\right)\left(x-3+\sqrt{x^2+x+2y-4}\right)=4\end{matrix}\right.\)
3)\(\left\{{}\begin{matrix}x-\dfrac{1}{x}=y-\dfrac{1}{y}\\2y=x^3+1\end{matrix}\right.\)
4)\(\left\{{}\begin{matrix}\sqrt{2x-3}=\left(y^2+2011\right)\left(5-y\right)+\sqrt{y}\\y\left(y-x+2\right)=3x+3\end{matrix}\right.\)
5)\(\left\{{}\begin{matrix}x^3+2x^2=x^2y+2xy\\2\sqrt{x^2-2y-1}+\sqrt[3]{y^3-14=x-2}\end{matrix}\right.\)
