\(\begin{cases} x^3+4y-y^3-16x=0\\y^2=5x^2+4\end{cases}\to \begin{cases} x^3-y^3=16x-4y=4(4x-y)(1)\\y^2-5x^2=4(2) \end{cases}\\(2), (1)\to x^3-y^3=(y^2-5x^2)(4x-y)\\\to x^3-y^3=4xy^2 - y^3 - 20x^3 +5x^2y\\\to 21x^3 - 4xy^2 - 5x^2y=0\\\to x(21x^2-4y^2 - 5xy)=0\\\to x (7x-4y)(3x+y)=0\\\to\left[ \begin{array}{l}x=0\\7x=4y\\3x=-y\end{array} \right.\\\bullet x=0\\\to y^2=4\to \left[ \begin{array}{l}y=2\\y=-2\end{array} \right.\\\bullet 7x=4y\\\to y=\dfrac{7x}{4}\\\to \dfrac{49x^2}{16}-5x^2-4=0\\\to \dfrac{-31}{16}x^2=4\text{(Loại)}\\\bullet 3x=-y\to y=-3x\\\to 9x^2 -5x^2=4\\\to x^2=1\to \left[ \begin{array}{l}x=1\\x=-1\end{array} \right.\\x=1\to y=-3\\x=-1\to y=3\\(x;y)=(0;2), (0;-2), (1;-3), (-1;3)\)
