x^{3}+y^{3}+z^3-3xyz=1/2(x+y+z)(x-y)^2+(y-z)^2+(z-x)^2 хәл итегез

$$x ^ { 3 } + y ^ { 3 } + z ^ { 3 } - 3 x y z = \frac { 1 } { 2 } ( x + y + z ) ( x - y ) ^ { 2 } + ( y - z ) ^ { 2 } + ( z - x ) ^ { 2 }$$

x өчен чишелеш (complex solution)

$$x=-\sqrt{-\left(z-y\right)^{2}}+z$$

$$x=2-z-y$$

$$x=\sqrt{-\left(z-y\right)^{2}}+z$$

y өчен чишелеш (complex solution)

$$y=-\sqrt{-\left(z-x\right)^{2}}+z$$

$$y=2-z-x$$

$$y=\sqrt{-\left(z-x\right)^{2}}+z$$

x өчен чишелеш

$$\left\{\begin{matrix}\\x=2-z-y\text{, }&\text{unconditionally}\\x=y\text{, }&y=z\end{matrix}\right.$$

y өчен чишелеш

$$\left\{\begin{matrix}\\y=2-z-x\text{, }&\text{unconditionally}\\y=x\text{, }&x=z\end{matrix}\right.$$