x^3-(x^2-x+1)
=x^3-x^2+x-1
=x^2(x-1)+(x-1)
=(x^2+1)(x-1)
x^2+1恒>0
x≥1 x-1≥0
x^3-(x^2-x+1)≥0
x^3≥x^2-x+1
当x=1时,取等号.
设x大于等于1,比较x的3次方与x的平方-x+1的大小.
x^3-(x^2-x+1)
=x^3-x^2+x-1
=x^2(x-1)+(x-1)
=(x^2+1)(x-1)
x^2+1恒>0
x≥1 x-1≥0
x^3-(x^2-x+1)≥0
x^3≥x^2-x+1
当x=1时,取等号.