Đáp án: $M=1$

Giải thích các bước giải:

Ta có:

$\dfrac{ab}{a+b}=\dfrac{bc}{b+c}=\dfrac{ca}{c+a}$

$\to \dfrac{a+b}{ab}=\dfrac{b+c}{bc}=\dfrac{c+a}{ca}$

$\to \dfrac1b+\dfrac1a=\dfrac1c+\dfrac1b=\dfrac1a+\dfrac1c$

$\to \dfrac1b+\dfrac1a=\dfrac1c+\dfrac1b\to \dfrac1a=\dfrac1c\to a=c$

      $\dfrac1c+\dfrac1b=\dfrac1a+\dfrac1c\to \dfrac1b=\dfrac1a\to b=a$

$\to a=b=c$

$\to M=\dfrac{3a^2}{3a^2}=1$