Question

[OoO Kún Chảnh OoO]

cho x,y,z là các số thỏa mãn :

x/y=2/3 ; y/z= 1/4 va 1/x+1/y+1/z= 1

hãy tìm x,y,z 

Answer 1

[✓ ℍɠŞ_ŦƦùM $₦G ✓]

\(\frac{x}{y}=\frac{2}{3}\Rightarrow\frac{x}{2}=\frac{y}{3};\frac{y}{z}=\frac{1}{4}\Rightarrow\frac{y}{1}=\frac{z}{4}\Rightarrow\frac{y}{3}=\frac{z}{12}\)

=>x=2k;y=3k;z=12k

thay vào ta có:

\(\frac{1}{2k}+\frac{1}{3k}+\frac{1}{12k}=1\)

\(\Rightarrow\frac{1}{2}.\frac{1}{k}+\frac{1}{3}.\frac{1}{k}+\frac{1}{12}.\frac{1}{k}=1\)

\(\Rightarrow\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{12}\right)\frac{1}{k}=1\)

\(\Rightarrow\frac{11}{12}.\frac{1}{k}=1\Rightarrow\frac{1}{k}=\frac{1}{\frac{11}{12}}\)

\(\Rightarrow x=\frac{11}{6};y=\frac{11}{4};z=11\)

Answer 2

[Edogawa Conan]

\(\frac{x}{y}=\frac{2}{3}\Rightarrow\frac{x}{2}=\frac{y}{3};\frac{y}{z}=\frac{1}{4}\Rightarrow\frac{y}{1}=\frac{z}{4}\Rightarrow\frac{y}{3}=\frac{z}{12}\)

\(\Rightarrow x=2k;y=3k;z=12k\)

Thay vào ta có:

\(\frac{1}{2k}+\frac{1}{3k}+\frac{1}{12k}=1\)

\(\Rightarrow\frac{1}{2}.\frac{1}{k}+\frac{1}{3}.\frac{1}{k}+\frac{1}{12}.\frac{1}{k}=1\)

\(\Rightarrow\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{12}\right)\frac{1}{k}=1\)
\(\Rightarrow\frac{11}{12}.\frac{1}{k}=1\Rightarrow\frac{1}{k}=\frac{1}{\frac{11}{12}}\)

\(\Rightarrow x=\frac{11}{6};y=\frac{11}{4};z=11\)