Đặt x/x+1=a; y/y+1=b
Theo đề, ta có hệ phương trình:
\(\left\{{}\begin{matrix}2a+b=3\\a+3b=-1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}a=2\\b=-1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2x+2\\y=-y-1\end{matrix}\right.\)
=>x=-2; y=-1/2
1)\(\left\{{}\begin{matrix}2x+\dfrac{1}{y}=\dfrac{3}{x}\\2y+\dfrac{1}{x}=\dfrac{3}{y}\end{matrix}\right.\)
2)\(\left\{{}\begin{matrix}x^3=3x+8y\\y^3=3y+8x\end{matrix}\right.\)
3)\(\left\{{}\begin{matrix}x^2+y^2+x-2y=2\\x^2+y^2+2x+2y=11\end{matrix}\right.\)
4)\(\left\{{}\begin{matrix}x^3-y=1\\3x^2-3xy+y^2=1\end{matrix}\right.\)
5)\(\left\{{}\begin{matrix}x^3-y^3=9\\\left(x-y\right)\left(x^2+y^2\right)=15\end{matrix}\right.\)
giai hpt
a.\(\left\{{}\begin{matrix}x=y+4\\2x+3=0\end{matrix}\right.\)
b.\(\left\{{}\begin{matrix}2x+y=7\\3y-x=7\end{matrix}\right.\)
c.\(\left\{{}\begin{matrix}5x+y=3\\-x-\dfrac{1}{5}y=\dfrac{-3}{5}\end{matrix}\right.\)
d.\(\left\{{}\begin{matrix}3x-5y=-18\\x-5=2y\end{matrix}\right.\)
Giải hệ PT \(\left\{{}\begin{matrix}\dfrac{x}{y}+2.\dfrac{y}{x}=3\\2x^2-3y=-1\end{matrix}\right.\)
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 hệ pt:
(1) \(\left\{{}\begin{matrix}x^2-3xy+2y^2=0\\3x+y=6\end{matrix}\right.\)
(2)\(\left\{{}\begin{matrix}\dfrac{x-1}{2x+1}-\dfrac{y-2}{y+2}=1\\\dfrac{3x-3}{2x+1}+\dfrac{2y-4}{y+2}=3\end{matrix}\right.\)
(3)\(\left\{{}\begin{matrix}2\left(x+y\right)+\sqrt{x+1}=4\\x+y-3\sqrt{x+1}=-5\end{matrix}\right.\)
Giải hệ
1) \(\left\{{}\begin{matrix}x-\dfrac{1}{x}=y-\dfrac{1}{y}\\2x^2-xy-1=0\end{matrix}\right.\)
2) \(\left\{{}\begin{matrix}y\left(4x^3+1\right)=3\\y^3\left(3x-1\right)=4\end{matrix}\right.\)
giải hệ phương trình
\(\left\{{}\begin{matrix}\sqrt{x-2}+\sqrt{y-3}=3\\2\sqrt{x-2}-3\sqrt{y-3}=-4\end{matrix}\right.\)
\(\left\{{}\begin{matrix}\dfrac{3x}{x+1}+\dfrac{2}{y+4}=4\\\dfrac{2x}{x+1}-\dfrac{5}{y+4}=4\end{matrix}\right.\)
giải hệ phương trình bằng pp sd bđt:
\(\left\{{}\begin{matrix}x+y^2+z^3=14\\\left(\dfrac{1}{2x}+\dfrac{1}{3y}+\dfrac{1}{6z}\right)\left(\dfrac{x}{2}+\dfrac{y}{3}+\dfrac{z}{6}\right)=1\end{matrix}\right.\)
\(\left\{{}\begin{matrix}\dfrac{2x^2}{x^2+1}=y\\\dfrac{3y^3}{y^4+y^2+y}=z\\\dfrac{4z^4}{z^6+z^4+z^2+1}=x\end{matrix}\right.\)
