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Ta có: $15(3x^2+5xy-4y^2)-38(5x^2-9xy-3y^2)=0$$\Leftrightarrow -145x^2+417xy+54y^2=0$$\Leftrightarrow (x-3y)(145x+18y)=0$$\Leftrightarrow \left[\begin{array}{l}x=3y\\x=\dfrac{-18}{145}y\end{array}\right.$Với $x=3y$ suy ra: $38y^2=38 \Leftrightarrow y=\pm1$Với $x=\dfrac{-18}{145}y$ suy ra: $\dfrac{-96178}{21025}y^2=38$, vô nghiệm.Suy ra:$(x;y)\in\{(1;3);(-1;-3)$

Ta có: $15(3x^2+5xy-4y^2)-38(5x^2-9xy-3y^2)=0$$\Leftrightarrow -145x^2+417xy+54y^2=0$$\Leftrightarrow (x-3y)(145x+18y)=0$$\Leftrightarrow \left[\begin{array}{l}x=3y\\x=\dfrac{-18}{145}y\end{array}\right.$Với $x=3y$ suy ra: $38y^2=38 \Leftrightarrow y=\pm1$Với $x=\dfrac{-18}{145}y$ $\Rightarrow \dfrac{-96178}{21025}y^2=38$, vô nghiệm.Suy ra:$(x;y) = (1;3);(-1;-3)$