Question

x/5=y/6; y/4=z/8 va 2x + 3y - 2 =36

Answer 1

\(\frac{x}{5}=\frac{y}{6}\) <=> \(\frac{x}{10}=\frac{y}{12}\)

\(\frac{y}{4}=\frac{z}{8}\) <=> \(\frac{y}{12}=\frac{z}{24}\)

=> \(\frac{x}{10}=\frac{y}{12}=\frac{z}{24}\) <=> \(\frac{2x}{20}=\frac{3y}{36}=\frac{z}{24}\)

Áp dụng tính chất của dãy ta có:

\(\frac{2x}{20}=\frac{3y}{36}=\frac{z}{24}=\frac{2x+3y-z}{20+36-24}=\frac{36}{32}=\frac{9}{8}\)

=> \(x=\frac{9}{8}.20:2=\frac{45}{4}\)

=> \(y=\frac{9}{8}.36:3=\frac{27}{2}\)

=> \(z=\frac{9}{8}.24=27\)