Question

[Taylor Swift]

Ba số x;y;z thỏa mãn \(\frac{6}{11}x=\frac{9}{2}y=\frac{18}{5}z\) và y+z-x=-120 

Khi đó : x+y=....

-chi tiết na-

Answer 1

[Minh Hiền]

\(\frac{6}{11}x=\frac{9}{2}y=\frac{18}{5}z\Rightarrow\frac{x}{\frac{11}{6}}=\frac{y}{\frac{2}{9}}=\frac{z}{\frac{5}{18}}\)

Theo t/c dãy TSBN:

\(\frac{x}{\frac{11}{6}}=\frac{y}{\frac{2}{9}}=\frac{z}{\frac{5}{18}}=\frac{y+z-x}{\frac{2}{9}+\frac{5}{18}-\frac{11}{6}}=\frac{-120}{-\frac{4}{3}}=90\)

=> \(\frac{x}{\frac{11}{6}}=90\Rightarrow x=90.\frac{11}{6}=165\)

=> \(\frac{y}{\frac{2}{9}}=90\Rightarrow y=90.\frac{2}{9}=20\)

Vậy x+y = 165+20 = 185.