Question

18x^2-3xy-5y=25

Answer 1

Bổ sung: \(x,y\in \mathbb{Z}\)

\(\Leftrightarrow18x^2-25=3xy+5y=y\left(3x+5\right)\\ \Leftrightarrow y=\dfrac{18x^2-25}{3x+5}=\dfrac{18x^2+30x-30x-50+25}{3x+5}\\ \Leftrightarrow y=\dfrac{6x\left(3x+5\right)-10\left(3x+5\right)+25}{3x+5}=6x-10+\dfrac{25}{3x+5}\)

Mà \(y\in \mathbb{Z}\) nên \(3x+5\in\left\{-25;-5;-1;1;5;25\right\}\)

\(\Leftrightarrow x\in\left\{-10;-2;0\right\}\)

Với \(x=-10\Leftrightarrow y=-71\)

Với \(x=-2\Leftrightarrow y=-47\)

Với \(x=0\Leftrightarrow y=-5\)

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