由原方程整理得3x^2+x+（M-2）2=0
设方程3x^2+x+（M-2）2=0的两个实数根分别为x1,x2
则x1+x2=-1/3,x1×x2=2(m-2)
∵(x1-x2)^2=(x1+x2)^2-4x1x2=(-1/3)^2-4×2×(m-2)=144/9-8m
∴144/9-8m=15
m=1/8
检验当m=1/8时,△＞0
因此,m=1/8
说明:(x1-x2)^2=x1^2-2x1x2+x2^2=x1^2+2x1x2+x2^2-2x1x2-2x1x2
=x1^2+2x1x2+x2^2-4x1x2==(x1+x2)^2-4x1x2