\(\frac{x}{3}\)=\(\frac{y}{4}\) ; \(\frac{y}{5}\)=\(\frac{z}{7}\) \(\Rightarrow\) \(\frac{x}{15}\)=\(\frac{y}{20}\) ; \(\frac{y}{20}\)=\(\frac{z}{28}\) \(\Rightarrow\) \(\frac{x}{15}\)=\(\frac{y}{20}\)=\(\frac{z}{28}\) \(\Rightarrow\) \(\frac{2x}{30}\)=\(\frac{3y}{60}\)=\(\frac{z}{28}\)
Ap dung tinh chat cua day ti so = nhau , ta co:
\(\frac{2x}{30}=\frac{3y}{60}=\frac{z}{28}=\frac{2x+3y-z}{30+60-28}=\frac{124}{62}=2\)
\(\Rightarrow\) \(2x=2.30\)\(=60\) \(\Rightarrow\) \(x=60:2=30\)
\(\Rightarrow\) \(3y=2.60=120\) \(\Rightarrow\) \(y=120:3=40\)
\(\Rightarrow\) \(z=2.28=56\)
\(\dfrac{x}{3}=\dfrac{y}{4};\dfrac{y}{5}=\dfrac{z}{7}\)
\(\Leftrightarrow\dfrac{x}{15}=\dfrac{y}{20}=\dfrac{z}{28}\)
\(\Leftrightarrow\dfrac{2x}{30}=\dfrac{3y}{60}=\dfrac{z}{28}\)
Áp dụng t/c dãy tỉ số bằng nhau ta có :
\(\dfrac{2x}{30}=\dfrac{3y}{60}=\dfrac{z}{28}=\dfrac{2x+3y-z}{30+60-28}=\dfrac{124}{62}=2\)
\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{2x}{30}=2\\\dfrac{3y}{60}=2\\\dfrac{z}{28}=2\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x=30\\y=40\\z=56\end{matrix}\right.\)
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