câu 1: giải hệ phương trình
\(\left(x+y\right)^2+\left(y+z\right)^4+....+\left(x+z\right)^{100}=-\left(y+z+x\right)\)
\(\left(xy\right)^2+2\left(yz\right)^4+....+100\left(zx\right)^{100}=-[\left(x+y+z\right)+2\left(yz+zx+xy\right)+......+99\left(x+y+z\right)]\)\(\left(\frac{1}{x}+\frac{1}{y}\right)^2+\left(\frac{1}{y^2}+\frac{1}{z^2}\right)^2+...+\left(\frac{1}{x^{99}}+\frac{1}{z^{99}}\right)^2=-\frac{1}{\left(xy\right)^2+2\left(yz\right)^2+.....+99\left(zx\right)^2}\)
tìm x,y,z
1.Giải hệ pt
1)\(\hept{\begin{cases}\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=3\\xy+yz+zx=3\\\frac{1}{1+x+xy}+\frac{1}{1+y+yz}+\frac{1}{1+z+zx}=x\end{cases}}\)
2)\(\hept{\begin{cases}xy+yz+zx=3\\\left(x+y\right)\left(y+z\right)=\sqrt{3}z\left(1+y^2\right)\\\left(y+z\right)\left(z+x\right)=\sqrt{3}x\left(1+z^2\right)\end{cases}}\)
3)\(\hept{\begin{cases}xy+yz+zx=3\\1+x^2\left(y+z\right)+xyz=4y\\1+y^2\left(z+x\right)+xyz=4z\end{cases}}\)
Giải hệ phương trình:
a)\(\hept{\begin{cases}\frac{xy}{x+y}=\frac{8}{3}\\\frac{yz}{y+z}=\frac{12}{5}\\\frac{zx}{z+x}=\frac{24}{7}\end{cases}}\)
b)\(\hept{\begin{cases}\frac{2x^2}{1+x^2}=y\\\frac{2y^2}{1+y^2}=z\\\frac{2z^2}{1+z^2}=x\end{cases}}\)
c)\(\hept{\begin{cases}\frac{xy}{x+y}=2-z\\\frac{yz}{y+z}=2-x\\\frac{zx}{z+x}=2-y\end{cases}}\)
xy+yz+zx=670
\(\frac{x}{x^2-yz+2010}+\frac{y}{y^2-zx+2010}+\frac{z}{z^2-xy+2010}\ge\frac{1}{x+y+z}giảipt\)
giải pt
Giải hệ phương trình
\(\hept{\begin{cases}\frac{xy}{x+y}=\frac{2}{3}\\\frac{yz}{y+z}=\frac{6}{5}\\\frac{zx}{z+x}=\frac{3}{4}\end{cases}}\)
1)giải phương trình \(\sqrt{8x+1}+\sqrt{46-10x}=-x^3+5x^2+4x+1\)
2)cho x,y,z>0 và xy+yz+zx=670 chứng minh
\(P=\frac{x}{x^2-yz+2010}+\frac{y}{y^2-xz+2010}+\frac{z}{z^2-xy+2010}\ge\frac{1}{x+y+z}\)
cho các số dương x;y;z thỏa mãn xy+yz+zx=670
CMR: \(\frac{x}{x^2-yz+2010}+\frac{y}{y^2-zx+2010}+\frac{z}{z^2-xy+2010}\ge\frac{1}{x+y+z}\)
Cho x,y,z > 0 ; x + y + z = 1
CMR: \(\sqrt{\frac{xy}{z+xy}}+\sqrt{\frac{yz}{x+yz}}+\sqrt{\frac{zx}{y+zx}}\le\frac{3}{2}\)
cho x,y,z dương sao cho \(xy+yz+zx=670\)
c/m \(\frac{x}{x^2-yz+2010}+\frac{y}{y^2-zx+2010}+\frac{z}{z^2-xy+2010}\ge\frac{1}{x+y+z}\)