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a) HPT
$\Leftrightarrow \begin{cases}12x^{2}y +6xy^{2} =90\\ 8x^{3} +y^{3} =35\end{cases}$
$\Leftrightarrow \begin{cases}xy(2x+y)=15\\ 8x^{3} +y^{3}+12x^{2}y +6xy^{2} =125\end{cases}$
$\Leftrightarrow \begin{cases}xy(2x+y)=15\\(2x+y)^3 =125\end{cases}$
$\Leftrightarrow \begin{cases}xy(2x+y)=15\\(2x+y) =5\end{cases}$
$\Leftrightarrow \begin{cases}xy=3\\2x+y =5\end{cases}$
$\Leftrightarrow \begin{cases}x(5-2x)=3\\y =5-2x\end{cases}$
$\Leftrightarrow (x,y)=(1,3), (3/2,2).$
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