Chủ đề này có 2 trả lời

[namdang248]

$\left\{\begin{matrix} x+y+z=1\\ \frac{1}{x}+\frac{1}{y}+\frac{1}{z}=1 \end{matrix}\right.$

[hoanglong2k]

$\left\{\begin{matrix} x+y+z=1\\ \frac{1}{x}+\frac{1}{y}+\frac{1}{z}=1 \end{matrix}\right.$

$HPT\Rightarrow \frac{1}{x+y+z}=\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\Rightarrow (x+y)(y+z)(z+x)=0\Leftrightarrow \begin{bmatrix} x+y=0;z=1\\ y+z=0;x=1\\ z+x=0;y=1 \end{bmatrix}$

[issacband365]

Vi x+y+z=1 $\Leftrightarrow$ $\frac{1}{x+y+z}=1$ $\Leftrightarrow$ $\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=\frac{1}{x+y+z}=1$

$\Leftrightarrow \frac{1}{x}+\frac{1}{y}=\frac{1}{x+y+z}-\frac{1}{z}$

$\Leftrightarrow \frac{x+y}{xy}=\frac{-(x+y)}{(x+y+z)z}$

Xet voi x+y=0 va x+y#0