x1²-3x1-k=0 (1)
x2²-3x2-k=0 (2)
(1)-(2)
(x1²-x2²)-3(x1-x2)=0
x1-x2=(x1²-x2²)/3=3/3=1
x1=x2+1
由韦达定理得
x1+x2=3 x1x2=-k
x1=x2+1代入x1+x2=3
2x2+1=3 2x2=2 x2=1
x1=x2+1=1+1=2
k=-x1x2=-1×2=-2
k的值是-2.