Question

若a,b是不等的正数,则ab^k+a^kb-(a^k+1+b^k+1)(k∈N^*)的符号是(    )

A.恒正                                     B.与k的奇偶有关

C.恒负                                     D.与a、b的大小有关

Answer 1

解析：ab^k+a^kb-(a^k+1+b^k+1)=a^k(b-a)+b^k(a-b)=(b-a)(a^k-b^k),

当a＞b时,有b-a＜0,a^k-b^k＞0,

则(a-b)(a^k-b^k)＜0.

当a＜b时,b-a＞0,a^k-b^k＜0,则(a-b)(a^k-b^k)＜0.

∴ab^k+a^kb-(a^k+1+b^k+1)＜0.

答案：C