\(\left\{{}\begin{matrix}4x^2-5xy-2y^2=4\\x^2+xy-y^2=5\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}20x^2-25xy-10y^2=20\\4x^2+4xy-4y^2=20\end{matrix}\right.\)
\(\Rightarrow16x^2-29xy-6y^2=0\)
\(\Leftrightarrow\left(x-2y\right)\left(16x+3y\right)=0\)
\(\Leftrightarrow...\)
giải hệ phương trình
\(\left\{{}\begin{matrix}\frac{x+y}{xy}+\frac{xy}{x+y}=\frac{5}{2}\\\frac{x-y}{xy}+\frac{xy}{x-y}=\frac{10}{3}\end{matrix}\right.\)
Giải hệ phương trình: \(\left\{{}\begin{matrix}x+\frac{1}{x}+y+\frac{1}{y}=\frac{9}{2}\\xy+\frac{1}{xy}=\frac{5}{2}\end{matrix}\right.\)
GIẢI HỆ PHƯƠNG TRÌNH ( Nâng cao )
\(1,\left\{{}\begin{matrix}x^2+y^2+\frac{1}{x^2}+\frac{1}{y^2}=5\\\left(xy-1\right)^2=x^2-y^2+2\end{matrix}\right.\)
\(2,\left\{{}\begin{matrix}\left(2-\frac{1}{2x+y}\right)\sqrt{y}=2\\\left(2+\frac{1}{2x+y}\right)\sqrt{x}=2\end{matrix}\right.\)
Giải hệ phương trình
a)\(\left\{{}\begin{matrix}2x^3=y+1\\2y^3=x+1\end{matrix}\right.\)
b)\(\left\{{}\begin{matrix}x^2+\frac{1}{y^2}+\frac{x}{y}=7\\x^2-\frac{1}{y^2}=3\end{matrix}\right.\)
c)\(\left\{{}\begin{matrix}x^2+y^2=10\\x+y=4\end{matrix}\right.\)
d)\(\left\{{}\begin{matrix}xy+x+y=19\\x^2y+xy^2=84\end{matrix}\right.\)
e)\(\left\{{}\begin{matrix}x^2+xy+y^2=4\\x+xy+y=2\end{matrix}\right.\)
Giải hệ phương trình
1. \(\left\{{}\begin{matrix}x^2+y^2+2x+2y=\left(x+2\right)\left(y+2\right)\\\left(\frac{x}{y+2}\right)^2+\left(\frac{y}{x+2}\right)^2=1\end{matrix}\right.\)
2. \(\left\{{}\begin{matrix}x^2-2xy-6=6y+2x\\\frac{3x^2}{y+1}=4-x\end{matrix}\right.\)
3.\(\left\{{}\begin{matrix}x^2-y=y^2-x\\x^2-x=y+3\end{matrix}\right.\)
4.\(\left\{{}\begin{matrix}x+y+\frac{1}{x}+\frac{1}{y}=\frac{9}{2}\\xy+\frac{1}{xy}+\frac{x}{y}+\frac{y}{x}=5\end{matrix}\right.\)
6.\(\left\{{}\begin{matrix}x^3\left(x-y\right)+x^2y^2=1\\x^2\left(xy+3\right)-3xy=3\end{matrix}\right.\)
7.\(\left\{{}\begin{matrix}x^2+3y-6x=0\\9x^2-6xy^2+y^4-3y+9=0\end{matrix}\right.\)
8.\(\left\{{}\begin{matrix}x^2+y^2+xy=1\\x+y-xy=2y^2-x^2\end{matrix}\right.\)
9.\(\left\{{}\begin{matrix}8x^3-y=y^3-2x\\x^2+y^2=x+2y\end{matrix}\right.\)
10.\(\left\{{}\begin{matrix}2x^2-3xy+y^2+x-y=0\\x^2+x+1=y^2\end{matrix}\right.\)
11.\(\left\{{}\begin{matrix}\left(x^2+y^2\right)\left(x+y+2\right)=4\left(y+2\right)\\x^2+y^2+\left(y+2\right)\left(x+y+2\right)=4\left(y+2\right)\end{matrix}\right.\)
12. \(\left\{{}\begin{matrix}x^2+7=4y^2+4y\\x^2+3xy+2y^2+x+y=0\end{matrix}\right.\)
13. \(\left\{{}\begin{matrix}x^2+y^2=5\\x^3+2y^3+\left(x-5\right)^2+\left(y+5\right)^2=55\end{matrix}\right.\)
14. \(\left\{{}\begin{matrix}\frac{1}{x^2}+\frac{1}{y^2}=3+x^2y^2\\\frac{1}{x^3}+\frac{1}{y^3}+3=x^3y^3\end{matrix}\right.\)
15.\(\left\{{}\begin{matrix}x^2+y^2+4x+2y=3\\x^2+7y^2-4xy+6y=13\end{matrix}\right.\)
16. \(\left\{{}\begin{matrix}x^2-5xy+x-5y^2=42\\7xy+6y^2+42=x\end{matrix}\right.\)
17.\(\left\{{}\begin{matrix}x^2+xy+y^2=13\\x^4+x^2y^2+y^4=91\end{matrix}\right.\)
18.\(\left\{{}\begin{matrix}x^2=\left(2-y\right)\left(2+y\right)\\2x^3=\left(x+y\right)\left(4-xy\right)\end{matrix}\right.\)
Đây là các bài hệ trong đề thi chuyên toán mong mọi người giúp vì mình bận quá nên không thể làm hết được ạ
Giải hệ phương trình sau
a. \(\left\{{}\begin{matrix}x^2+y^2+2\left(x+y\right)=23\\x+y+xy=11\end{matrix}\right.\)
b. \(\left\{{}\begin{matrix}x^2+4x+y=0\\\left(x+2\right)^2+5y=16\end{matrix}\right.\)
c. \(\left\{{}\begin{matrix}x+y+\frac{1}{x}+\frac{1}{y}=5\\x^2+y^2+\frac{1}{x^2}+\frac{1}{y^2}=9\end{matrix}\right.\)
Giải hpt : a) \(\left\{{}\begin{matrix}xy^2+2x+y=4xy\\\frac{1}{xy}+\frac{1}{y^2}+\frac{y}{x}=3\end{matrix}\right.\)
b) \(\left\{{}\begin{matrix}x^2+y^2+\frac{4y}{x}=22\\\frac{3}{x^2+y^2-1}+\frac{2x}{y}=1\end{matrix}\right.\)
Giải hệ phương trình: \(\left\{{}\begin{matrix}2x-y-xy=13\\15\left(\frac{1}{x+1}+\frac{1}{y-2}\right)=2\end{matrix}\right.\)
giải hệ phương trình \(\left\{{}\begin{matrix}\left(\frac{x}{y}\right)^2+\left(\frac{x}{y}\right)^3=12\\\left(xy\right)^2+xy=6\end{matrix}\right.\)
Giải hệ phương trình :
1, \(\left\{{}\begin{matrix}\frac{2}{x}+\frac{3}{y-2}=4\\\frac{4}{x}+\frac{1}{y-2}=1\end{matrix}\right.\)
2 , \(\left\{{}\begin{matrix}\frac{2}{2x-y}-\frac{1}{x+y}=0\\\frac{3}{2x-y}-\frac{6}{x+y}=-1\end{matrix}\right.\)
3, \(\left\{{}\begin{matrix}5\left(x+2y\right)=3x-1\\2x+4=3\left(x-2y\right)-15\end{matrix}\right.\)
4, \(\left\{{}\begin{matrix}2x+y=7\\-x+4y=10\end{matrix}\right.\)
