Đặt:
\(\dfrac{x}{3}=\dfrac{y}{5}=k\)
\(\Rightarrow\left\{{}\begin{matrix}x=3k\\y=5k\end{matrix}\right.\)
\(\Rightarrow xy=3k.5k=135\)
\(\Rightarrow15k^2=135\)
\(\Rightarrow k^2=9\)
\(\Rightarrow k=\pm3\)
\(\Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x=3.3=9\\y=3.5=15\end{matrix}\right.\\\left\{{}\begin{matrix}x=-3.3=-9\\y=-3.5=-15\end{matrix}\right.\end{matrix}\right.\)
Vậy....
Đặt \(\dfrac{x}{3}=\dfrac{y}{5}=k\Rightarrow\left\{{}\begin{matrix}x=3k\\y=5k\end{matrix}\right.\)
Suy ra \(xy=135\Rightarrow3k\cdot15k=135\)
\(\Rightarrow45k^2=135\Rightarrow k^2=3\Rightarrow k=\pm\sqrt{3}\)
*)Xét \(k=\sqrt{3}\)\(\Rightarrow\left\{{}\begin{matrix}x=3k=3\cdot\sqrt{3}=3\sqrt{3}\\y=5k=5\cdot\sqrt{3}=5\sqrt{3}\end{matrix}\right.\)
*)Xét \(k=-\sqrt{3}\)\(\Rightarrow\left\{{}\begin{matrix}x=3k=-3\cdot\sqrt{3}=-3\sqrt{3}\\y=5k=-5\cdot\sqrt{3}=-5\sqrt{3}\end{matrix}\right.\)
Ta có : \(\dfrac{x}{3}=\dfrac{y}{5}\) và xy = 135
\(\Rightarrow\dfrac{x}{3}.y=\dfrac{y}{5}.y\Leftrightarrow\dfrac{xy}{3}=\dfrac{y^2}{5}\)
\(\Rightarrow\dfrac{135}{3}=\dfrac{y^2}{5}\Rightarrow y^2=\dfrac{135}{3}.5=225=\left(\pm15\right)^2\)* Nếu y = 15 \(\Rightarrow\dfrac{x}{3}=\dfrac{15}{5}\Rightarrow x=9\)
* Nếu y = -15 \(\Rightarrow\dfrac{x}{3}=\dfrac{-15}{5}\Rightarrow x=-9\)
Vậy có 2 bộ số (x,y) là (-9,-15);(9,15)
tik mik nha
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