Question

tìm x,y,z biết 5x = 2 y, 2 x= 3z và x.y = 90

Answer 1

Giải:

\(5x=2y\Leftrightarrow\dfrac{x}{2}=\dfrac{y}{5}\Leftrightarrow\dfrac{x}{6}=\dfrac{y}{15}\)

\(2x=3z\Leftrightarrow\dfrac{x}{3}=\dfrac{z}{2}\Leftrightarrow\dfrac{x}{6}=\dfrac{z}{4}\)

\(\Leftrightarrow\dfrac{x}{6}=\dfrac{y}{15}=\dfrac{z}{4}\)

Đặt: \(\dfrac{x}{6}=\dfrac{y}{15}=\dfrac{z}{4}=k\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=6k\\y=15k\end{matrix}\right.\)

\(xy=90\Leftrightarrow6k.15k=90k^2=90\Leftrightarrow k=\pm1\)

TH1: \(k=1\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=6\\y=15\\z=4\end{matrix}\right.\)

TH1: \(k=-1\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=-6\\y=-15\\z=-4\end{matrix}\right.\)

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