梯形螺杆规格:若A=1+2X^4,B=X^2+2X^3,那么A和B的大小关系为?

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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)
=(x-1)^2*(x^2+2x+1+x^2)
=(x-1)^2*[(x+1)^2+x^2]>0 所以A>B

A-B=2X^4-2X^3-X^2+1
=(X-1)^2(2X^2+2X+1)
前一因式当且仅当X=1时为0,后一因式恒大于0
故A大于等于B