Question

tim x y z biet \(\frac{x-4}{2}\)=\(\frac{y-6}{3}\)=\(\frac{z-8}{4}\)va x+y+z=27

 

 

Answer 1

\(\frac{x}{2}-2=\frac{y}{3}-2=\frac{z}{4}-2\)

\(\Rightarrow\frac{x}{2}=\frac{y}{3}=\frac{z}{4}\Rightarrow\frac{x}{2}=\frac{y}{3}=\frac{z}{4}=\frac{x+y+z}{2+3+4}=\frac{27}{9}=3\)
\(\Rightarrow x=6,y=9,z=12\)

Answer 2

Áp dụng tính chất dãy tỉ số bằng nhau ,ta có:

\(\frac{x-4}{2}=\frac{y-6}{3}=\frac{z-8}{4}=\frac{x+y+z-18}{2+3+4}=1\)

Ta có:\(\frac{x-4}{2}=1\Rightarrow x=6\)

\(\frac{y-6}{3}=1\Rightarrow y=9\)

\(\frac{z-8}{4}=1\Rightarrow z=12\)

Answer 3

Áp dụng tính chất tỉ lệ thức, ta có:

\(\frac{x-4}{2}=\frac{y-6}{3}=\frac{z-8}{4}=\frac{x+y+z-18}{9}=\frac{27-18}{9}=1\)

\(\Rightarrow\hept{\begin{cases}\frac{x-4}{2}=1\Leftrightarrow x=6\\\frac{y-6}{3}=1\Leftrightarrow y=9\\\frac{z-8}{4}=1\Leftrightarrow z=12\end{cases}}\)