x1,x2是方程x²+x-3=0的两根,所以x1+x2=-1,x1x2=-3.
因为x²+x-3=0,所以x³+x²-3x=0,x³=-x²+3x
x1³-x2²+30=-x1²+3x1-x2²+30
=(x1-x2)(x1+x2)+3x1+30
=-(x1-x2)+3x1+30
=2x1+x2+30
=x1+29.
x1,x2是方程x²+x-3=0的两根,所以x1+x2=-1,x1x2=-3.
因为x²+x-3=0,所以x³+x²-3x=0,x³=-x²+3x
x1³-x2²+30=-x1²+3x1-x2²+30
=(x1-x2)(x1+x2)+3x1+30
=-(x1-x2)+3x1+30
=2x1+x2+30
=x1+29.