Toán Lớp 7: tính x-y-z biết 5x=4y,4x=5zvaf x.y.z=-64
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Toán Lớp 7: tính x-y-z biết 5x=4y,4x=5zvaf x.y.z=-64
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\left\{ \begin{array}{l}
5x = 4y\\
4x = 5z
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
\dfrac{x}{4} = \dfrac{y}{5} \Leftrightarrow \dfrac{x}{{20}} = \dfrac{y}{{25}}\\
\dfrac{x}{5} = \dfrac{z}{4} \Leftrightarrow \dfrac{x}{{20}} = \dfrac{z}{{16}}
\end{array} \right.\\
\Leftrightarrow \dfrac{x}{{20}} = \dfrac{y}{{25}} = \dfrac{z}{{16}} = k\\
\Leftrightarrow \left\{ \begin{array}{l}
x = 20k\\
y = 25k\\
z = 16k
\end{array} \right.\left( {k \ne 0} \right)\\
x.y.z = – 64\\
\Leftrightarrow 20k.25.k.16k = – 64\\
\Leftrightarrow {k^3} = – \dfrac{1}{{125}} = {\left( { – \dfrac{1}{5}} \right)^3}\\
\Leftrightarrow k = – \dfrac{1}{5}\\
\Leftrightarrow \left\{ \begin{array}{l}
x = – \dfrac{1}{5}.20 = – 4\\
y = – \dfrac{1}{5}.25 = – 5\\
z = – \dfrac{1}{5}.16 = – \dfrac{{16}}{5}
\end{array} \right.\\
\Leftrightarrow x – y – z\\
= – 4 – \left( { – 5} \right) – \left( { – \dfrac{{16}}{5}} \right)\\
= – 4 + 5 + \dfrac{{16}}{5}\\
= \dfrac{{21}}{5}
\end{array}$