\(\frac{3}{4}x=\frac{4}{5}y=\frac{6}{7}z\Leftrightarrow\frac{x}{\frac{4}{3}}=\frac{y}{\frac{5}{4}}=\frac{z}{\frac{7}{6}}\)
Áp dụng tính chất dãy tỉ số bằng nhau , ta có:
\(\frac{x}{\frac{4}{3}}=\frac{y}{\frac{5}{4}}=\frac{z}{\frac{7}{6}}=\frac{z+y+z}{\frac{4}{3}+\frac{5}{4}+\frac{7}{6}}=\frac{-45}{\frac{15}{4}}=-12\)
=> x = 4/3 . (-12) = -16
=> y = 5/4 . (-12) = -15
=> z = 7/6 . (-12) =-14
\(\frac{3}{4}x=\frac{4}{5}y\Rightarrow\frac{x}{\frac{4}{5}}=\frac{y}{\frac{3}{4}}\left(1\right)\)
\(\frac{4}{5}y=\frac{6}{7}z\Rightarrow\frac{y}{\frac{6}{7}}=\frac{z}{\frac{4}{5}}\left(2\right)\)
Từ (1) và (2) => \(\frac{x}{\frac{24}{35}}=\frac{y}{\frac{9}{14}}=\frac{z}{\frac{3}{5}}\).
Theo t/c dãy tỉ số = nhau:
\(\frac{x}{\frac{24}{35}}=\frac{y}{\frac{9}{14}}=\frac{z}{\frac{3}{5}}=\frac{x+y+z}{\frac{24}{35}+\frac{9}{14}+\frac{3}{5}}=-\frac{45}{\frac{27}{14}}=-\frac{70}{3}\).
=> \(\frac{x}{\frac{24}{35}}=-\frac{70}{3}\Rightarrow x=-\frac{70}{3}.\frac{24}{35}=-16\)
=>\(\frac{y}{\frac{9}{14}}=-\frac{70}{3}\Rightarrow y=-\frac{70}{3}.\frac{9}{14}=-15\)
=>\(\frac{z}{\frac{3}{5}}=-\frac{70}{3}\Rightarrow z=-\frac{70}{3}.\frac{3}{5}=-14\)
Vậy x=-16; y=-15; z=-14.
