Question

已知关于x的方程x³-(2m+1)x²+(3m+2)x-m-2=0（1）证明x=1是方程的解（2）把

Answer 1

x³-(2m+1)x²+(3m+2)x-m-2=x³-x²+2x-2-2mx²+3mx-m

=x²(x-1)+2(x-1)-m(2x²-3x+1)

=x²(x-1)+2(x-1)-m(x-1)(2x-1)

=x²(x-1)+2(x-1)-m(x-1)(2x-1)

=(x-1)[x²+2-m(2x-1)]

=(x-1)(x²-2mx+m+2)

因此x=1是方程的解