1+2x^4-(2x^3+x^2)
=2x^3(x-1)-(x^2-1)
=(x-1)(2x^3-2x+x-1)
=(x-1)[2x(x^2-1)+x-1]
=(x-1)^2[2x*(x+1)+1]
=(x-1)^2*(2x^2+2x+1)
由于2x^2+2x+1=0的判别式小于0,
所以,该式恒大于0
所以,x=1时,两式相等,x≠1时,1+2x^4>2x^3+x^2
综上：1+2x^4>=2x^3+x^2