若A=1+2X^4,B=X^2+2X^3,那么A和B的大小关系为?
问题描述：
若A=1+2X^4,B=X^2+2X^3,那么A和B的大小关系为?
答
A－B=2x^4-2x^3-x^2+1=(x-1)*2x^3-(x-1)*(x+1)=(x-1)*[2x^3-x-1]=(x-1)*[x^3-x+x^3-1]=(x-1)[x(x^2-1)+(x-1)(x^2+x+1)]=(x-1)[x(x-1)(x+1)+(x-1)(x^2+x+1)]=(x-1)[(x-1)x(x+1)+(x-1)(x^2+x+1)]=(x-1)^2*(2x^2+2x+1)=...