Ta có: \(\dfrac{x}{2}=\dfrac{2y}{3}=\dfrac{xy}{2y}=\dfrac{27}{2y}\)
\(\Rightarrow\dfrac{2y}{3}=\dfrac{27}{2y}\Rightarrow\left(2y\right)^2=27.3\)
\(\Rightarrow4y^2=81\Rightarrow y^2=20,25\)
\(\Rightarrow\left\{{}\begin{matrix}y=4,5\\y=-4,5\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=\dfrac{27}{4,5}=6\\x=\dfrac{27}{-4,5}=-6\end{matrix}\right.\)
\(\Rightarrow x^2+y^2=6^2+4,5^2=\left(-6\right)^2+\left(-4,5\right)^2=56,25\)
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