Question

Tìm 3 số x,y,z biết: \(\dfrac{4}{x+1}=\dfrac{2}{y-2}=\dfrac{3}{z+2}\) và xyz=12

Answer 1

\(\dfrac{4}{x+1}=\dfrac{2}{y-2}=\dfrac{3}{z+3}\)

\(\Leftrightarrow\dfrac{x+1}{4}=\dfrac{y-2}{2}=\dfrac{z+2}{3}\)

Đặt \(\dfrac{x+1}{4}=\dfrac{y-2}{2}=\dfrac{z+2}{3}\)\(=k\Leftrightarrow\left\{{}\begin{matrix}x=4k-1\\y=2k+2\\z=3k-3\end{matrix}\right.\)

Mà \(xyz=12\)

\(\Leftrightarrow4k-1+2k+2+3k-3=12\)

\(\Leftrightarrow9k-2=12\)

\(\Rightarrow k=\dfrac{14}{9}\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{47}{9}\\y=\dfrac{46}{9}\\z=\dfrac{5}{3}\end{matrix}\right.\)

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