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
问题描述：
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
答
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=z4x^2/(1+4...