Question

已知abc=1,求证：a/(ab+a+1)+b/(bc+a+1)+c/(ca+c+1)=1

Answer 1

题目写错了吧,应该是b/(bc+b+1)啊

证明：因为abc=1

所以b=1/ac

ab=1/c

bc=1/a

所以

a/(ab+a+1)+b/(bc+b+1)+c/(ca+c+1)

=a/(1/c+a+1)+(1/ac)/(1/a+1/ac+1)+c/(ac+c+1)

=ac/(ac+c+1)+1/(ac+c+1)+c/(ac+c+1)

=(ac+c+1)/(ac+c+1)

=1

所以a/(ab+a+1)+b/(bc+b+1)+c/(ca+c+1)=1