Question

方程x² -3x-2=0有2根X1,X2,求x1³ -x2³

Answer 1

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