已知a,b,c满足ab+a+b=ac+c+a=3,求(a+1)(b+1)(c+1)的值

ab+a+b=bc+b+c=ac+a+c=3,则ab+a+b+1=bc+b+c+1=ac+a+c+1=4于是,a(b+1)+b+1=(a+1)(b+1)=4,同理得：(b+1)(c+1)=4,(c+1)(a+1)=4三式相乘得：[（a+1)(b+1)(c+1)]²=4×4×4=64所以：（a+1)(b+1)(c+1)=8