Question

若a、b、c均大于0,且abc=1,则(a/ab+a+1)+(b/bc+b+1)+(c/ca+c+1)=______

Answer 1

因为：a/(ab+a+1)＝a/(ab+a+abc)=1/(b+1+bc)

可知:a/(ab+a+1)=1/b *b/(bc+b+1)

又有:c/(ca+c+1)=c/(ca+c+abc)=1/(a+1+ab)=1／a* a/(ab+a+1)

=1／a* 1/b *b/(bc+b+1)=1/ab* b/(bc+b+1)

所以：a/(ab+a+1) +b/(bc+b+1) +c/(ca+c+1)

＝1/b *b/(bc+b+1)+b/(bc+b+1)+1/ab* b/(bc+b+1)

=(a+ab+abc)/(a+ab+abc)

=1