（1）由a=x²-x+1＞0,b=x²-2x＞0,c=2x-1＞0,解得x＞2；这时,a-b=x+1＞0,则a＞b；a-c=x²-3x+2=（x-1）（x-2）＞0,则a＞c,a为最大边.又由b+c＞a,即（x²-2x）+（2x-1）＞x²-x+1,得x＞2.则实数x...