Question

bài 1 tìm các số x,y,z

a,5x=8y=20z và x-y-z=3

b,\(\dfrac{6}{11}\)x=\(\dfrac{9}{2}y=\dfrac{18}{5}z\)và -x+y+z=-120

Answer 1

\(5x=8y=20z\)

\(\Leftrightarrow\dfrac{x}{\dfrac{1}{5}}=\dfrac{y}{\dfrac{1}{8}}=\dfrac{z}{\dfrac{1}{20}}\)

dựa vào t/c của dãy tỉ số = nhau ta có:

\(\dfrac{x}{\dfrac{1}{5}}=\dfrac{y}{\dfrac{1}{8}}=\dfrac{z}{\dfrac{1}{20}}\Leftrightarrow=\dfrac{x-y-z}{\dfrac{1}{5}-\dfrac{1}{8}-\dfrac{1}{20}}\)

Mà x-y-z=3

\(\Leftrightarrow\dfrac{x-y-z}{\dfrac{1}{5}-\dfrac{1}{8}-\dfrac{1}{20}}=\dfrac{3}{\dfrac{1}{5}-\dfrac{1}{8}-\dfrac{1}{20}}=\dfrac{3}{\dfrac{1}{40}}=120\)

\(x=120.\dfrac{1}{5}=24\)

\(y=120.\dfrac{1}{8}=15\)

\(z=120.\dfrac{1}{20}=6\)

Vây...