Question

Tìm x; y; z biết:
2x=3y=5z và 2x+3y-z=15

Answer 1

\(2x=3y=5z\)

\(\Leftrightarrow\dfrac{2x}{30}=\dfrac{3y}{30}=\dfrac{5z}{30}\)

\(\Leftrightarrow\dfrac{2x}{30}=\dfrac{3y}{30}=\dfrac{z}{6}\)

Áp dụng t,c dãy tỉ số bằng nhau ta có :

\(\dfrac{2x}{30}=\dfrac{3y}{30}=\dfrac{z}{6}=\dfrac{2x+3y-z}{30+30-6}=\dfrac{15}{54}\) \(=\dfrac{5}{18}\)

\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{2x}{30}=\dfrac{5}{18}\\\dfrac{3y}{30}=\dfrac{5}{18}\\\dfrac{z}{6}=\dfrac{5}{18}\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{25}{6}\\y=\dfrac{25}{9}\\z=\dfrac{5}{3}\end{matrix}\right.\)

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