x=2z²/(1+z²),y =2x²/(1+x²),z =2y²/(1+y²).解方程组,
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![x=2z²/(1+z²),y =2x²/(1+x²),z =2y²/(1+y²).解方程组,](/uploads/image/z/1641347-35-7.jpg?t=x%3D2z%26%23178%3B%2F%281%2Bz%26%23178%3B%29%2Cy+%3D2x%26%23178%3B%2F%281%2Bx%26%23178%3B%29%2Cz+%3D2y%26%23178%3B%2F%281%2By%26%23178%3B%EF%BC%89.%E8%A7%A3%E6%96%B9%E7%A8%8B%E7%BB%84%2C)
x=2z²/(1+z²),y =2x²/(1+x²),z =2y²/(1+y²).解方程组,
x=2z²/(1+z²),y =2x²/(1+x²),z =2y²/(1+y²).解方程组,
x=2z²/(1+z²),y =2x²/(1+x²),z =2y²/(1+y²).解方程组,
显然x=y=z=0是它的解
当xyz≠0时,x,y,z>0
∴x=2z²/(1+z²)≤2z²/(2z﹚=z(,当且仅当z=1时取=)
同理y≤x,z≤y
∴x≤z≤y≤x(,当且仅当x=y=z=1时取=)
∴x=y=z=1
即原方程组的解是x=y=z=0和x=y=z=1.