1, \(\left\{{}\begin{matrix}x^3+2y^2-4y+29=0\\x^2+x^2y^2-18y=0\end{matrix}\right.\)
2, \(\left\{{}\begin{matrix}x^3+2y^2-4y+10=0\\x^2+x^2y^2-16y+12=0\end{matrix}\right.\)
3, \(\left\{{}\begin{matrix}x,y>0\\x+y=7\\\dfrac{9}{x}+\dfrac{16}{y}=7\end{matrix}\right.\)
4, \(\left\{{}\begin{matrix}x,y>0\\x+y=4\\\dfrac{4}{x}+\dfrac{9}{y}\le4\end{matrix}\right.\)
5, \(\left\{{}\begin{matrix}x^3+y^2=\dfrac{211}{27}\\x^2+y^2+xy-3x-4y+4=0\end{matrix}\right.\)
6, \(\left\{{}\begin{matrix}x^4+81y^2=697\\x^2+9y^2+3xy-9x-36y+36=0\end{matrix}\right.\)
1/Ghpt\(\left\{{}\begin{matrix}x^2+y^2+x^2y^2=1+2xy\\\left(x-y\right)\left(1+xy\right)=1-xy\end{matrix}\right.\)
2/Ghpt\(\left\{{}\begin{matrix}x^2y+y+xy^2+x=18xy\\x^4y^2+y^2+x^2y^4+x^2=208x^2y^2\end{matrix}\right.\)
3/Ghpt\(\left\{{}\begin{matrix}\sqrt{x+3}+\sqrt{y+3}=4\\\dfrac{1}{x}+\dfrac{1}{y}=2\end{matrix}\right.\)
4/ Cho x,y là nghiệm của hệ phương trình
\(\left\{{}\begin{matrix}x+y=m\\x^2+y^2=2m\end{matrix}\right.\)
Tìm min và max của A=xy
5/cho x,y,z thỏa mãn đk
\(\left\{{}\begin{matrix}xy+yz+xz=1\\x^2+y^2+z^2=2\end{matrix}\right.\)
Chứng minh rằng: \(\dfrac{-4}{3}\le x,y,z\le\dfrac{4}{3}\)
6/Ghpt bằng 3 cách\(\left\{{}\begin{matrix}x+y+z=1\\\\x^2+y^2+z^2=1\\x^3+y^3+z^3=1\end{matrix}\right.\)
7/Ghpt\(\left\{{}\begin{matrix}x^3+1=2y\\y^3+1=2x\end{matrix}\right.\)
8/Ghpt\(\left\{{}\begin{matrix}x^2-3y=-2\\y^2-3x=-2\end{matrix}\right.\)
9/Ghpt bằng 2 cách\(\left\{{}\begin{matrix}x+\sqrt{y+3}=3\\y+\sqrt{x+3}=3\end{matrix}\right.\)
10/Ghpt\(\left\{{}\begin{matrix}x+\dfrac{2}{y}=\dfrac{3}{x}\\y+\dfrac{2}{x}=\dfrac{3}{y}\end{matrix}\right.\)
11/Ghpt\(\left\{{}\begin{matrix}\sqrt[3]{3x+5}=y+1\\\sqrt[3]{3y+5}=x+1\end{matrix}\right.\)
12/Ghpt\(\left\{{}\begin{matrix}3x^2y-y^2-2=0\\3y^2x-x^2-2=0\end{matrix}\right.\)
13/Giải các phương trình sau bằng cách đứa về hệ pt đối xứng loại II:
a)\(\left(x^2-3\right)^2-x-3=0\)
b)\(x^2-2=\sqrt{x+2}\)
14/Ghpt:\(\left\{{}\begin{matrix}x^2+y^2+xy=3\\x^2-y^2+xy=1\end{matrix}\right.\)
Giải hệ phương trình
a. \(\left\{{}\begin{matrix}\dfrac{1}{2}\left(x+2\right)\left(y+3\right)-\dfrac{1}{2}xy=50\\\dfrac{1}{2}xy-\dfrac{1}{2}\left(x-2\right)\left(y-2\right)=32\end{matrix}\right.\)
b. \(\left\{{}\begin{matrix}\dfrac{3x+5}{x+1}-\dfrac{2}{y+4}=4\\\dfrac{2x}{x+1}-\dfrac{5y+9}{y+4}=9\end{matrix}\right.\)
c. \(\left\{{}\begin{matrix}x^2+y^2-2x-2y-23=0\\x-3y-3=0\end{matrix}\right.\)
d.\(\left\{{}\begin{matrix}\left(x-y\right)^2-3x-3y=4\\2x+y=3\end{matrix}\right.\)
giải hệ sau bằng phương pháp thế
a)\(\left\{{}\begin{matrix}2x-y=4\\x+5y=3\end{matrix}\right.\)
b)\(\left\{{}\begin{matrix}-2x+3y=-1\\x+2y=3\end{matrix}\right.\)
giải hệ sau:
a)\(\left\{{}\begin{matrix}x+y=-1\\2x+y=1\end{matrix}\right.\)
b)\(\left\{{}\begin{matrix}\dfrac{1}{x}+\dfrac{1}{y}=\dfrac{1}{5}\\\dfrac{3}{x}+\dfrac{4}{y}=2\end{matrix}\right.\)
c)\(\left\{{}\begin{matrix}2\dfrac{5}{x-1}+\dfrac{3}{3y-2}=1\\\dfrac{2}{2x-1}+\dfrac{1}{3y-2}=1\end{matrix}\right.\)
Giải các hệ phương trình sau:a) \(\left\{{}\begin{matrix}\left(2x-y\right)^2-6x+3y=0\\x+2y=0\end{matrix}\right.\);b) \(\left\{{}\begin{matrix}\sqrt{\dfrac{2x-y}{x+y}}+\sqrt{\dfrac{x+y}{2x-y}}=2\\3x+y=14\end{matrix}\right.\)
Giải các hệ phương trình :
1) \(\left\{{}\begin{matrix}2x+3y=5\\4x+6y=10\end{matrix}\right.\) 2) \(\left\{{}\begin{matrix}\dfrac{3x}{x+1}-\dfrac{2}{y+4}=4\\\dfrac{2x}{x+1}-\dfrac{5}{y+4}=9\end{matrix}\right.\)
giải hệ phương trình: \(\left\{{}\begin{matrix}\dfrac{x^2}{16}+\dfrac{y^2}{4}+\dfrac{xy}{x+2y}=1\\\sqrt{x^2+16}+\dfrac{5}{2}\sqrt{x+2y}=2x+\sqrt{x^2+7}\end{matrix}\right.\)
giải hệ phương trình:
a)\(\left\{{}\begin{matrix}\dfrac{x+1}{x-1}+\dfrac{3y}{y+2}=7\\\dfrac{2}{x-1}-\dfrac{5}{y+2}=4\end{matrix}\right.\)
b)\(\left\{{}\begin{matrix}2\left(x^2-2x\right)+\sqrt{y+1}=0\\3\left(x^2-2x\right)-2\sqrt{y+1}=-7\end{matrix}\right.\)
Giai he phuong trinh:
a) \(\left\{{}\begin{matrix}5x+3y=31\\\sqrt{\dfrac{x+2}{y-3}}+\sqrt{\dfrac{y-3}{x+2}}=2\end{matrix}\right.\)
b) \(\left\{{}\begin{matrix}\dfrac{x}{y}-\dfrac{x}{y+12}=1\\\dfrac{x}{y-12}-\dfrac{x}{y}=2\end{matrix}\right.\)