Đáp án:
M=2017
Giải thích các bước giải:
\(\begin{array}{l}
\frac{{a + b}}{3} = \frac{{b + c}}{4} = \frac{{c + a}}{5} = \frac{{a + b + b + c + c + a}}{{3 + 4 + 5}} = \frac{{a + b + c}}{6}\\
= \frac{{a + b + b + c}}{{3 + 4}} = \frac{{a + 2b + c}}{7}\\
= \frac{{b + c + a + c}}{{4 + 5}} = \frac{{a + b + 2c}}{9}\\
= \frac{{a + b + a + c}}{{3 + 5}} = \frac{{2a + b + c}}{8}\\
\to \frac{{a + b + c}}{6} = \frac{{a + 2b + c}}{7} = \frac{{a + b + 2c}}{9} = \frac{{2a + b + c}}{8}\\
= \frac{{2a + b + c - a - b - c}}{{8 - 6}} = \frac{a}{2}\\
= \frac{{a + 2b + c - a - b - c}}{{7 - 6}} = \frac{b}{1}\\
= \frac{{a + b + 2c - a - b - c}}{{9 - 6}} = \frac{c}{3}\\
\to \frac{a}{2} = \frac{b}{1} = \frac{c}{3}\\
\to a = 2b,c = 3b\\
M = 10a + b - 7c + 2017 = 20b + b - 21b + 2017 = 2017
\end{array}\)
