解決{l}{(y+2)(x+y+z)=1}{(z+x)(x+y+z)=3}{(x+y)(x+y+z)=4} |Microsoft數學求解器

$$\left. \begin{array} { l } { ( y + 2 ) ( x + y + z ) = 1 } \\ { ( z + x ) ( x + y + z ) = 3 } \\ { ( x + y ) ( x + y + z ) = 4 } \end{array} \right.$$

解 y、x、z

$$x=\frac{11-3\sqrt{5}}{4}\approx 1.072949017\text{, }y=\frac{-\sqrt{5}-7}{4}\approx -2.309016994\text{, }z=-2$$

$$x=\frac{3\sqrt{5}+11}{4}\approx 4.427050983\text{, }y=\frac{\sqrt{5}-7}{4}\approx -1.190983006\text{, }z=-2$$