Tính M = x + y + z

Lời giải:

Từ đề bài suy ra: \(\frac{1}{{x + y}} + \frac{1}{{y + z}} + \frac{1}{{z + x}} = \frac{{133}}{{10}}:19 = \frac{{17}}{{10}}\)

Từ đề bài suy ra: \(\frac{x}{{y + z}} + \frac{y}{{x + z}} + \frac{z}{{x + y}} = \frac{{133}}{{10}}:7 = \frac{{19}}{{10}}\)

\(\begin{array}{l}\frac{x}{{y + z}} + 1 + \frac{y}{{x + z}} + 1 + \frac{z}{{x + y}} + 1 = \frac{{19}}{{10}} + 3\\(x + y + z)(\frac{1}{{x + y}} + \frac{1}{{y + z}} + \frac{1}{{z + x}}) = \frac{{49}}{{10}}\\(x + y + z).\frac{{17}}{{10}} = \frac{{49}}{{10}}\\x + y + z = \frac{{49}}{{17}}\end{array}\)