∵y=x²-x+

1

x

=x（x-1）+1-

x-1

x

=1+

x2(x-1)-(x-1)

x

=1+

(x-1)(x2-1)

x

=1+

(x-1)2(x+1)

x

，

∵x为正整数，

∴

(x-1)2(x+1)

x

≥0，

当x=1时，

(x-1)2(x+1)

x

=0，

∴y=1+

(x-1)2(x+1)

x

≥1．

∴函数y=x2-x+

1

x

的最小值是1．