Pt đầu phân tích được đó: x2 + 2xy - 3y2 = (x2 + 2xy + y2) - 4y2 = (x + y)2 - (2y)2 = (x + 3y)(x - y) = 0
<=> x = y hoặc x = 3y
Thay vào pt dưới rồi xét TH thôi :)
1, Giải các hệ phương trình sau
a, \(\left\{{}\begin{matrix}\left(x+y\right)^2-2xy=26\\x+y=6\end{matrix}\right.\)
b,\(\left\{{}\begin{matrix}2x^2+x-y=0\\xy+3y-5x=7\end{matrix}\right.\)
c, \(\left\{{}\begin{matrix}\left(x-1\right)^2=1-y\\\left(x^2-y\right)^2=2xy\left(1+x\right)\end{matrix}\right.\)
d, \(\left\{{}\begin{matrix}x^2y+y^2x=2\\x^3+y^3+6=8x^2y^2\end{matrix}\right.\)
giải hệ phương trình:
1, \(\left\{{}\begin{matrix}\left(x+1\right)^2+y^2+xy+y=4\\x+2y+xy=1\end{matrix}\right.\)
2, \(\left\{{}\begin{matrix}x^2+2y^2-3x+2xy=0\\xy\left(x+y\right)+\left(x-1\right)^2=3y\left(1-y\right)\end{matrix}\right.\)
3, \(\left\{{}\begin{matrix}14x^2-21y^2+22x-39y=0\\35x^2+28y^2+111x-10y=0\end{matrix}\right.\)
Giaỉ hệ phương trình
1) \(\left\{{}\begin{matrix}x^2-2xy+x+y=0\\x^4-x^2\left(4y-3\right)+y^2=0\end{matrix}\right.\)
2)\(\left\{{}\begin{matrix}3x^2+2xy+y^2=11\\x^2+2xy+3y^2=17\end{matrix}\right.\)
3)\(\left\{{}\begin{matrix}x^3-2y^3-x-4y=0\\13x^2-41xy+21y^2+9=0\end{matrix}\right.\)
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 hệ phương trình \(\left\{{}\begin{matrix}\left(2x+y\right)y+1-4y=0\\xy\left(x+y\right)+x-3y=0\end{matrix}\right.\)
Giải hệ phương trình:
\(\left\{{}\begin{matrix}\left(x+y\right)^2=xy+3y-1\\x+y=\dfrac{x^2+y+1}{1+x^2}\end{matrix}\right.\)
Giải hệ phương trình:
1. \(\left\{{}\begin{matrix}x+3=2\sqrt{\left(3y-x\right)\left(y+1\right)}\\\sqrt{3y-2}-\sqrt{\dfrac{x+5}{2}}=xy-2y-2\end{matrix}\right.\)
2. \(\left\{{}\begin{matrix}\sqrt{2y^2-7y+10-x\left(y+3\right)}+\sqrt{y+1}=x+1\\\sqrt{y+1}+\dfrac{3}{x+1}=x+2y\end{matrix}\right.\)
3. \(\left\{{}\begin{matrix}\sqrt{4x-y}-\sqrt{3y-4x}=1\\2\sqrt{3y-4x}+y\left(5x-y\right)=x\left(4x+y\right)-1\end{matrix}\right.\)
4. \(\left\{{}\begin{matrix}9\sqrt{\dfrac{41}{2}\left(x^2+\dfrac{1}{2x+y}\right)}=3+40x\\x^2+5xy+6y=4y^2+9x+9\end{matrix}\right.\)
5. \(\left\{{}\begin{matrix}\sqrt{xy+\left(x-y\right)\left(\sqrt{xy}-2\right)}+\sqrt{x}=y+\sqrt{y}\\\left(x+1\right)\left[y+\sqrt{xy}+x\left(1-x\right)\right]=4\end{matrix}\right.\)
6. \(\left\{{}\begin{matrix}x^4-x^3+3x^2-4y-1=0\\\sqrt{\dfrac{x^2+4y^2}{2}}+\sqrt{\dfrac{x^2+2xy+4y^2}{3}}=x+2y\end{matrix}\right.\)
7. \(\left\{{}\begin{matrix}x^3-12z^2+48z-64=0\\y^3-12x^2+48x-64=0\\z^3-12y^2+48y-64=0\end{matrix}\right.\)
Giải các hệ phương trình:
a, \(\left\{{}\begin{matrix}-2x+y=xy\\2x+3y=2xy\end{matrix}\right.\)
\(b,\left\{{}\begin{matrix}\left(\sqrt{2}+1\right)x-\left(2-\sqrt{3}\right)y=2\\\left(2+\sqrt{3}\right)x+\left(\sqrt{2}-1\right)y=2\end{matrix}\right.\)
giải hệ phương trình
a)\(\left\{{}\begin{matrix}\left(x^2+1\right)\left(y^2+1\right)=10\\\left(x+y\right)\left(xy-1\right)=3\end{matrix}\right.\)
b)\(\left\{{}\begin{matrix}x^2+y^2+2\left(xy-2\right)=0\\x^2+y^2-2xy=16\end{matrix}\right.\)
c)\(\left\{{}\begin{matrix}x^2-2x\sqrt{y}+2y=x\\y^2-2y\sqrt{x}+2z=y\\z^2-2z\sqrt{x}+2x=z\end{matrix}\right.\)
