设5x^2+2x-3=0的两根为x1,x2,则
x1+x2=-2/5,x1x2=-3/5,
-1/x1^2-1/x2^2=-(x1^2+x2^2)/(x1x2)^2=-[(x1+x2)^2-2x1x2]/(x1x2)^2
=-(4/25+6/5)/(9/25)=-34/9,
(-1/x1^2)(-1/x2^2)=1/(x1x2)^2=25/9,
∴所求的新方程为x^2+(34/9)x+25/9=0,即9x^2+34x+25=0.