Question

cho a+b+c= 2009 và 1/a+b  +1/ b+c   +1/ c+a = 1/7. Tính S= a/b+c  +b/c+a  +c/a+b=?

Answer 1

\(\frac{a}{b+c}+1+\frac{b}{a+c}+1+\frac{c}{a+b}+1=\frac{2a}{a+b+c}+\frac{2b}{a+b+c}+\frac{2c}{a+b+c}=\frac{2\left(a+b+c\right)}{a+b+c}=2\)

=>S=2-1-1-1=-1

Answer 2

a/b+c +1 +b/a+c +1 +c/a+b +1

=a+b+c/b+c+  a+b+c/a+c+  a+b+c/a+b

=2009.1/7

=287