حل {c}{|8+x|=2+y}{y+z=30}{yzx=60}

$$\left. \begin{array} { c } { | 8 + x | = 2 + y } \\ { y + z = 30 } \\ { y z x = 60 } \end{array} \right.$$

حل مسائل x، y، z

$$x=2\left(2\sqrt{21}\cos(\frac{\arccos(\frac{103\sqrt{21}}{588})}{3})+3\right)\approx 23.916140049\text{, }y=4\left(\sqrt{21}\cos(\frac{\arccos(\frac{103\sqrt{21}}{588})}{3})+3\right)\approx 29.916140049\text{, }z=2\left(-2\sqrt{21}\cos(\frac{\arccos(\frac{103\sqrt{21}}{588})}{3})+9\right)\approx 0.083859951$$

$$x=2\left(-3\sqrt{7}\sin(\frac{\arccos(\frac{103\sqrt{21}}{588})}{3})-\sqrt{21}\cos(\frac{\arccos(\frac{103\sqrt{21}}{588})}{3})+3\right)\approx -6.313505065\text{, }y=2\left(-3\sqrt{7}\sin(\frac{\arccos(\frac{103\sqrt{21}}{588})}{3})-\sqrt{21}\cos(\frac{\arccos(\frac{103\sqrt{21}}{588})}{3})+6\right)\approx -0.313505065\text{, }z=2\left(3\sqrt{7}\sin(\frac{\arccos(\frac{103\sqrt{21}}{588})}{3})+\sqrt{21}\cos(\frac{\arccos(\frac{103\sqrt{21}}{588})}{3})+9\right)\approx 30.313505065$$

$$x=2\left(3\sqrt{7}\sin(\frac{\arccos(\frac{103\sqrt{21}}{588})}{3})-\sqrt{21}\cos(\frac{\arccos(\frac{103\sqrt{21}}{588})}{3})+3\right)\approx 0.397365016\text{, }y=2\left(3\sqrt{7}\sin(\frac{\arccos(\frac{103\sqrt{21}}{588})}{3})-\sqrt{21}\cos(\frac{\arccos(\frac{103\sqrt{21}}{588})}{3})+6\right)\approx 6.397365016\text{, }z=2\left(\sqrt{21}\cos(\frac{\arccos(\frac{103\sqrt{21}}{588})}{3})-3\sqrt{7}\sin(\frac{\arccos(\frac{103\sqrt{21}}{588})}{3})+9\right)\approx 23.602634984$$

$$x=\frac{10\left(-2\sqrt{13}\cos(\frac{\arccos(\frac{3581\sqrt{13}}{16900})}{3})-5\right)}{3}\approx -40.049854909\text{, }y=\frac{20\left(\sqrt{13}\cos(\frac{\arccos(\frac{3581\sqrt{13}}{16900})}{3})+1\right)}{3}\approx 30.049854909\text{, }z=\frac{10\left(-2\sqrt{13}\cos(\frac{\arccos(\frac{3581\sqrt{13}}{16900})}{3})+7\right)}{3}\approx -0.049854909$$

$$x=\frac{10\left(\sqrt{13}\cos(\frac{\arccos(\frac{3581\sqrt{13}}{16900})}{3})-\sqrt{39}\sin(\frac{\arccos(\frac{3581\sqrt{13}}{16900})}{3})-5\right)}{3}\approx -9.797231198\text{, }y=\frac{10\left(\sqrt{39}\sin(\frac{\arccos(\frac{3581\sqrt{13}}{16900})}{3})-\sqrt{13}\cos(\frac{\arccos(\frac{3581\sqrt{13}}{16900})}{3})+2\right)}{3}\approx -0.202768802\text{, }z=\frac{10\left(\sqrt{13}\cos(\frac{\arccos(\frac{3581\sqrt{13}}{16900})}{3})-\sqrt{39}\sin(\frac{\arccos(\frac{3581\sqrt{13}}{16900})}{3})+7\right)}{3}\approx 30.202768802$$