由韦达定理,得x1+x2=-1x1x2=-1(1)x1²+x2²=(x1+x2)²-2x1x2=(-1)²-2(-1)=1+2=3(2)(x1-x2)²=(x1+x2)²-4x1x2=(-1)²-4(-1)=1+4=5|x1-x2|=√5第一题中，怎么变成(x1+x2)2-2x1x2 的？第二题中又怎么变成(x1+x2)2-4x1x2的？这是利用韦达定理解题的最基本的恒等变换。x1²+x2²=x1²+2x1x2+x2²-2x1x2=(x1+x2)²-2x1x2(x1-x2)²=x1²-2x1x2+x2²=x1²+2x1x2+x2²-4x1x2=(x1+x2)²-4x1x2