x²-3x-2=0
x1+x2=3,x1x2=-2
x²=3x+2
x1²=3x1+2,x2²=3x2+2
x1³-x2³=x1*x1²-x2*x2²=x1(3x1+2)-x2(3x2+2)
=3(x1²+x2²)+2(x1+x2)
=3[(x1+x2)²-2x1x2]+2(x1+x2)
=3(9+4)+6=45