x1+x2=k-1x1x2=k+2则x1²+x2²=(x1+x2)²-2x1x2=6k²-2k+1-2k-4=6k²-4k-9=0k=2±√13有解则(k-1)²-4(k+2)>=0k²-6k-7>=0(k-7)(k+1)>=0k=7所以k=2-√13