- 问题详情:已知正数a,b,c,满足ab+a+b=bc+b+c=ca+c+a=99,则(a+1)(b+1)(c+1)= .【回答】1000.【解答】解:∵ab+a+b=bc+b+c=ca+c+a=99,∴ab+a+b+1=bc+b+c+1=ca+c+a+1=100,∴(a+1)(b+1)=(b+1)(c+1)=(a+1)(c+1)=100,∴(a+1)(b+1)(b+1)(c+1)(a+1)(c+1)=1000000,因为abc为正数,等式两边同时开方得,(a+1)(b+1)(c+1)=1000.知识点:整式...
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