Question

Tìm ba số x, y, z, biết rằng:

\(\frac{x}{2}=\frac{y}{3},\frac{y}{4}=\frac{z}{5}\)và x + y - z = 10

Tìm hai số x, y, biết rằng:

\(\frac{x}{2}=\frac{y}{5}\)và xy = 10

Answer 1

\(dat:\frac{x}{2}=\frac{y}{5}=k\)

x=2k   ;  y=5k

x.y=10k²

10 = 10k²

k² = 1

k  = +-1

Voi : k=1 = > x=1.2=2 ; y=5.1=5

voi : k=-1 => x=-1.2=-2 ; y=-1.5=-5

Answer 2

\(\frac{x}{2}=\frac{y}{3};\frac{y}{4}=\frac{z}{5}\Rightarrow\frac{x}{2}=\frac{4y}{12};\frac{3y}{12}=\frac{z}{5}\Rightarrow\frac{x}{8}=\frac{y}{12};\frac{y}{12}=\frac{z}{15}\Rightarrow\frac{x}{8}=\frac{y}{12}=\frac{z}{15}\)

Ap dung tinh chat day ti so bang nhau ta co : 

\(\frac{x}{8}=\frac{y}{12}=\frac{z}{15}=\frac{x+y-z}{8+12-15}=\frac{10}{5}=2\)

Suy ra  : \(\frac{x}{8}=2\Rightarrow x=16;\frac{y}{12}=2\Rightarrow y=2.12=24;\frac{z}{15}=2\Rightarrow z=2.15=30\)

nhieu qua lam ko het