\(x^2-\left(3y-2\right)x+2y^2-4y=0\)
\(\Delta=\left(3y-2\right)^2-4\left(2y^2-4y\right)=y^2+4y+4=\left(y+2\right)^2\)
\(\Rightarrow\left[{}\begin{matrix}x=\frac{3y-2+y+2}{2}=2y\\x=\frac{3y-2-y-2}{2}=y-2\end{matrix}\right.\)
Thế xuống dưới:
\(\Rightarrow\left[{}\begin{matrix}4y^2+y^2-2y^2+2y-5=0\\\left(y-2\right)^2+y^2-y\left(y-2\right)+2y-5=0\end{matrix}\right.\)
\(\Leftrightarrow...\)
Giải hệ phương trình: \(\left\{{}\begin{matrix}x^2+2y^2-3xy-2x+4y=0\\\left(x^2-5\right)^2=2x-2y+5\end{matrix}\right.\)
Giải hệ phương trình : \(\left\{{}\begin{matrix}x^2+y^2+x+y=8\\2x^2+y^2-3xy+3x-2y+1=0\end{matrix}\right.\)
giải hệ phương trình
a) \(\left\{{}\begin{matrix}3x-2y+z=14\\2x+y-z=3\\z-2x=-5\end{matrix}\right.\)
b) \(\left\{{}\begin{matrix}x^2-y^2=4y+2x+3\\x^2+2x+y=0\end{matrix}\right.\)
c)\(\left\{{}\begin{matrix}\left|xy-4\right|=8-y^2\\xy=2+x^2\end{matrix}\right.\)
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
\(a,\left\{{}\begin{matrix}\left(x+\sqrt{x^2+1}\right)\left(y+\sqrt{y^2+1}\right)=1\\y+\frac{y}{\sqrt{x^2-1}}=\frac{35}{12}\end{matrix}\right.\)
\(b,\left\{{}\begin{matrix}\left(x^2+y^2\right)\left(x+y+1\right)=25\left(y+1\right)\\x^2+xy+2y^2+x-8y=9\end{matrix}\right.\)
\(c,\left\{{}\begin{matrix}2x^2+3xy-2y^2-5\left(2x-y\right)=0\\x^2-2xy-3y^2+15=0\end{matrix}\right.\)
giải hpt
\(\left\{{}\begin{matrix}x^2+2y^2-3xy-2x+4y=0\\\left(x^2-5\right)^2=2x-2y+5\end{matrix}\right.\)
giải hệ phương trình:
1, \(\left\{{}\begin{matrix}x^2+y^2-xy+4y+1=0\\y\left(7-x^2-y^2+2xy\right)=2\left(x^2+1\right)\end{matrix}\right.\)
2, \(\left\{{}\begin{matrix}x^2+2y-4x=0\\4x^2-4xy^2+y^4-2y+4=0\end{matrix}\right.\)
Giải hệ pt
a) \(\left\{{}\begin{matrix}x^3+6x^2y=7\\2y^3+3xy^2=5\end{matrix}\right.\)
b) \(\left\{{}\begin{matrix}6x-xy-2=0\\2\sqrt{\left(x+2\right)\left(3x-y\right)}=y+6\end{matrix}\right.\)
giải hệ phương trình \(\left\{{}\begin{matrix}xy^2+3x^2=2y\\x^2y+y^2=-2x\end{matrix}\right.\)
