原方程两根为x1,x2
x1+x2=-3/2
x1x2=-1/2
新方程两根为y1,y2
y1=1/(x1+x2)=-2/3
y2=(x1-x2)^2=(x1+x2)^2-4x1x2=9/4+2=17/4
y1+y2=-2/3+17/4=43/12
y1y2=-2/3*17/4=-17/6
故y1,y2的方程为y^2-43y/12-17/6=0
即12y^2-43y-34=0