Question

Tìm x , y ,z biết :

a)   \(\frac{6}{11}x=\frac{9}{2}y=\frac{18}{5}z\)      và      \(-x+y+z=-120\)

b)     \(\frac{x}{12}=\frac{y}{9}=\frac{z}{5}\)     và        \(xyz=20\)

c)    \(\frac{12x-15y}{7}=\frac{20z-12x}{9}=\frac{15y-20z}{11}\)     và      \(x+y+z=48\)

Answer 1

b) Đặt \(\frac{x}{12}=\frac{y}{9}=\frac{z}{5}=k\)

\(\Rightarrow x=12k,y=9k,z=5k\)

\(xyz=20\)

\(\Rightarrow12k.9k.5k=20\)

\(\Rightarrow540k^3=20\)

\(\Rightarrow k^3=\frac{1}{27}\)

\(\Rightarrow k=\frac{1}{3}\)

Khi   \(k=\frac{1}{3}\)

\(\Rightarrow\frac{x}{12}=\frac{1}{3}\Rightarrow x=4\)

\(\frac{y}{9}=\frac{1}{3}\Rightarrow y=3\)

\(\frac{z}{5}=\frac{1}{3}\Rightarrow z=\frac{5}{3}\)

Vậy x = ..... ; y = ............ ; z = .............