已知实数x,y,z满足4x^2/1+4x^2=y,4y^2/1+4y^2=z,4z^2/1+4z^2=x,求x,y,z的值

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已知实数x,y,z满足4x^2/1+4x^2=y,4y^2/1+4y^2=z,4z^2/1+4z^2=x,求x,y,z的值
已知实数x,y,z满足4x^2/1+4x^2=y,4y^2/1+4y^2=z,4z^2/1+4z^2=x,求x,y,z的值

已知实数x,y,z满足4x^2/1+4x^2=y,4y^2/1+4y^2=z,4z^2/1+4z^2=x,求x,y,z的值
考察函数:f(x)=4x^2/(1+4x^2)
则有f(x)=y f(y)=z f(z)=x
不妨设:x>=y>=z
对:f(x)=4x^2/(1+4x^2)
=1/【1+1/4x^2】 当x增加时 f(x)显然增加
故为严格增函数
因为x>=y>=z
故f(x)>=f(y)>=f(z)
y>=z>=x
故x=y=z
4x^2/(1+4x^)=x
x=0或1/2
故x=y=z=0
或x=y=z=1/2