\(M=\frac{ab}{a+b}=\frac{bc}{b+c}=\frac{ca}{c+a}=\frac{ab+bc+ca}{a+b+b+c+c+a}=\frac{10a+b+10b+c+10c+a}{\left(a+a\right)+\left(b+b\right)+\left(c+c\right)}\)
\(=\frac{\left(10a+a\right)+\left(10b+b\right)+\left(10c+c\right)}{2a+2b+2c}=\frac{11a+11b+11c}{2a+2b+2c}=\frac{11.\left(a+b+c\right)}{2.\left(a+b+c\right)}=\frac{11}{2}\)
vậy M=11/2
$M=\frac{ab}{a+b}=\frac{bc}{b+c}=\frac{ca}{c+a}=\frac{ab+bc+ca}{a+b+b+c+c+a}=\frac{10a+b+10b+c+10c+a}{\left(a+a\right)+\left(b+b\right)+\left(c+c\right)}$M=aba+b =bcb+c =cac+a =ab+bc+caa+b+b+c+c+a =10a+b+10b+c+10c+a(a+a)+(b+b)+(c+c)
$=\frac{\left(10a+a\right)+\left(10b+b\right)+\left(10c+c\right)}{2a+2b+2c}=\frac{11a+11b+11c}{2a+2b+2c}=\frac{11.\left(a+b+c\right)}{2.\left(a+b+c\right)}=\frac{11}{2}$=(10a+a)+(10b+b)+(10c+c)2a+2b+2c =11a+11b+11c2a+2b+2c =11.(a+b+c)2.(a+b+c) =112
vậy M=11/2