Question

tìm x y z

5x=10y=12z biet x-y+z=100

\(\frac{x}{5}=\frac{y}{6}=\frac{z}{9}\)

biet x.y.z=270

Answer 1

a) ta có: \(5x=10y\Rightarrow\frac{x}{10}=\frac{y}{5}\Rightarrow\frac{x}{120}=\frac{y}{60}\)

\(10y=12z\Rightarrow\frac{y}{12}=\frac{z}{10}\Rightarrow\frac{y}{60}=\frac{z}{50}\)

\(\Leftrightarrow\frac{x}{120}=\frac{y}{60}=\frac{z}{50}\)

ADTCDTSBN

có: \(\frac{x}{120}=\frac{y}{60}=\frac{z}{50}=\frac{x-y+z}{120-60+50}=\frac{100}{110}=\frac{10}{11}\)

=> x/120 = 10/11 => ...

...

rùi bn tự lm típ nha!

Answer 2

b) ta có: \(\frac{x}{5}=\frac{y}{6}=\frac{z}{9}=k\Rightarrow\hept{\begin{cases}x=5k\\y=6k\\z=9k\end{cases}}\)

mà xyz = 270

=> 5k.6k.9k = 270

270.k³ = 270

=> k³ = 1

=> k = 1

=> x = 5k => x = 5

y = 6k => y = 6

z = 9k => z = 9

KL:...