已知正数a、b、c满足ab+a+b=bc+b+c=ac+a+c=3,则(a+1)(b+1)(c+1)=_.
问题描述:
已知正数a、b、c满足ab+a+b=bc+b+c=ac+a+c=3,则(a+1)(b+1)(c+1)=______.
答
由题意得ab+a+b=3,
∴(a+1)(b+1)=4,
同理可得(b+1)(c+1)=4,
(a+1)(c+1)=4,
∴[(a+1)(b+1)(c+1)]2=4×4×4,
∵a、b、c为正数,
∴(a+1)(b+1)(c+1)=8.
故答案为:8.