Question

tim ba so x,y,z biet

5x=8y=20z

va x-y-z=3

Answer 1

Ta có:         5x=8y=20z suy ra \(\frac{x}{\frac{1}{5}}\)=\(\frac{y}{\frac{1}{8}}\)=\(\frac{z}{\frac{1}{20}}\)

Áp dụng tính chất của dãy tỉ số bằng nhau ta có:

   \(\frac{X}{\frac{1}{5}}\)=\(\frac{Y}{\frac{1}{8}}\)=\(\frac{Z}{\frac{1}{20}}\)=\(\frac{X-Y-Z}{\frac{1}{5}-\frac{1}{8}-\frac{1}{20}}\)=\(\frac{3}{\frac{1}{40}}\)=120 (Vì x-y-z=3)

\(\frac{x}{\frac{1}{5}}\)=120 suy ra x=120.\(\frac{1}{5}\)=24

\(\frac{y}{\frac{1}{8}}\)=120 suy ra y=120.\(\frac{1}{8}\)=15

\(\frac{z}{\frac{1}{20}}\)=120 suy ra z=120.\(\frac{1}{20}\)=6