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#f1df3cf0-a78b-447f-803d-93cba17b4b74中等解答题幂函数函数

28.已知函数f(x)=4x24mx+m+2f(x)=4x^{2}-4mx+m+2
(1)若f(x)f(x)的图象与xx轴的两个不同交点的横坐标分别为x1x_{1}x2x_{2},求x12+x22x_1^2+x_2^2的取值范围;
(2)若f(x)=4x24mx+m+2f(x)=4x^{2}-4mx+m+2((-\infty1]1]上是减函数,且对任意的x1x_{1}x2[2x_{2}\in [-2m+1]m+1],总有f(x1)f(x2)64\vert f(x_{1})-f(x_{2})\vert \leqslant 64成立,求实数mm的取值范围.