Ta có : $3x^2 + 2y^2 - 7xy + 3x - y - 47 = 0$
$\Leftrightarrow 6x^2 + 4y^2 - 14xy + 6x - 2y- 94 = 0$
$\Leftrightarrow 4y^2 - 14xy + \frac{49}{4}x^2 - 2(2y-\frac{7}{2}x).\frac{1}{2} + \frac{1}{4} - \frac{25}{4}(x^2-2x.\frac{1}{5} + \frac{1}{25}) = 94$
$\Leftrightarrow (2y-\frac{7}{2}x-\frac{1}{2})^2 - \frac{25}{4}(x-\frac{1}{5})^2 = 94$
$\Leftrightarrow (2y-\frac{7}{2}x-\frac{1}{2}-\frac{5}{2}x+\frac{1}{2})(2y-\frac{7}{2}x-\frac{1}{2} + \frac{5}{2}x-\frac{1}{2}) = 94$
$\Leftrightarrow (2y-6x)(2y-x-1) = 94$
$\Leftrightarrow (y-3x)(2y-x-1) = 47$
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