题目

Mother’s Day is a holiday for mothers. It is celebrated in the United States, England and some other countries. In a short time, it has become a festival in many other countries. Mother’s Day comes on the second Sunday in May. On that day, many people send gifts to their mothers. Those whose mothers are still living often wear a pink or red rose or carnation(康乃馨), while those whose mothers are dead(死) wear a white one. The idea of a day for mothers was first given by Anna Jarvis of Philadelphia. As a result of her hard work, the first American Mother’s Day was held in Phil已知函数f（x）=21nx+ax2-1 （a∈R）（I）求函数f（x）的单调区间；（Ⅱ）若a=l，试解答下列两小题．（i）若不等式f（1+x）+f（1-x）＜m对任意的0＜x＜l恒成立，求实数m的取值范围；（ii）若x1，x2是两个不相等的正数，且以f（x1）+f（x2）=0，求证：x1+x2＞2．