Giải hệ phương trình
\(\left\{{}\begin{matrix}x^3-y^3=37\left(x-y\right)\\y^3-z^3=19\left(y-z\right)\\z^3-x^3=28\left(z-x\right)\end{matrix}\right.\)
Giải hệ phương trình
\(\left\{{}\begin{matrix}x+y+z=3\\\left(z+y\right)\left(y-3\right)\left(z-3\right)\end{matrix}\right.\)
Giải hệ phương trình:
\(\left\{{}\begin{matrix}x^2\left(y-z\right)=-\dfrac{5}{3}\left(1\right)\\y^2\left(z-x\right)=3\left(2\right)\\z^2\left(x-y\right)=\dfrac{1}{3}\left(3\right)\end{matrix}\right.\)
Giải HPT
1)\(\left\{{}\begin{matrix}x^2+y^2+z=1\\x^2+y+z^2=1\\x+y^2+z^2=1\end{matrix}\right.\)
2)
\(\left\{{}\begin{matrix}xyz=x+y+z\\yzt=y+z+t\\ztx=z+t+x\\txy=t+x+y\end{matrix}\right.\)
3)
\(\left\{{}\begin{matrix}x^3+y^2=2\\x^2+xy+y^2-y=0\end{matrix}\right.\)
4)\(\left\{{}\begin{matrix}x^2y^2-2x+y^2=0\\2x^2-4x+y^3+3=0\end{matrix}\right.\)
Giải hệ PT \(\left\{{}\begin{matrix}x+y+z=1\\x^2+y^2+z^2=1\\x^3+y^3+z^3=1\end{matrix}\right.\)
Giải hệ phương trình tìm nghiệm nguyên:
\(\left\{{}\begin{matrix}\left(2-x\right)\left(3x-2z\right)=3-z\\y^3+3y=x^2-3x+2\\z^2+y^2=6z\\z\le3\end{matrix}\right.\)
Giải hệ phương trình:
a)\(\left\{{}\begin{matrix}x\left(y-z\right)=4\\y\left(z-x\right)=9\\z\left(x+y\right)=1\end{matrix}\right.\)
giải các hệ phương trình sau:
a) \(\left\{{}\begin{matrix}\dfrac{1}{x}+\dfrac{1}{y+z}=\dfrac{1}{2}\\\dfrac{1}{y}+\dfrac{1}{z+x}=\dfrac{1}{3}\\\dfrac{1}{z}+\dfrac{1}{x+y}=\dfrac{1}{4}\end{matrix}\right.\)
b) \(\left\{{}\begin{matrix}\dfrac{x}{y}-\dfrac{y}{x}=\dfrac{5}{6}\\x^2-y^2=5\end{matrix}\right.\)
c) \(\left\{{}\begin{matrix}\dfrac{5}{\sqrt{x-7}}+\dfrac{3}{\sqrt{y+6}}=\dfrac{13}{6}\\\dfrac{7}{\sqrt{x-7}}-\dfrac{2}{\sqrt{y+6}}=\dfrac{5}{3}\end{matrix}\right.\)
\(\left\{{}\begin{matrix}\left(x+y\right)\left(y+z\right)=4xy^2z\\\left(y+z\right)\left(z+x\right)=4yz^2x\\\left(z+x\right)\left(x+y\right)=4zx^2y\end{matrix}\right.\)