Question

設(shè)不等的兩個(gè)正數(shù)a,b滿足a³-b³=a²-b²,則a+b的取值范圍是(    )

A.(1,+∞)             B.(1,)                C.［1,］              D.(0,1］

Answer 1

解析：由a³-b³=a²-b²,得a²+ab+b²=a+b,即(a+b)²-(a+b)-ab=0,

又∵()²＞ab,

∴(a+b)²-(a+b)-()²＜0,

即(a+b)²-(a+b)＜0,

∴1＜a+b＜.

答案：B