Question

Cho\(\frac{x}{2}=\frac{y}{3}=\frac{z}{5}\)

Và        xyz=810

Tìm x, y, z

Answer 1

Ta có:

\(\frac{x}{2}=\frac{y}{3}=\frac{z}{5}\)

=> \(\frac{x}{2}.\frac{x}{2}.\frac{x}{2}=\frac{y}{3}.\frac{y}{3}.\frac{y}{3}=\frac{z}{5}.\frac{z}{5}.\frac{z}{5}=\frac{x}{2}.\frac{y}{3}.\frac{z}{5}\)

=> \(\frac{x^3}{8}=\frac{y^3}{27}=\frac{z^3}{125}=\frac{810}{30}=27\)

=> \(\hept{\begin{cases}x^3=27.8=6^3\\y^3=27.27=9^3\\z^3=27.125=15^3\end{cases}}\)=> \(\hept{\begin{cases}x=6\\y=9\\z=15\end{cases}}\)

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