Tìm số cặp số nguyên x, y sao cho xy – 3x + 5y = 0.

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1. $xy-3x+5y=0$

   $⇒xy-3x+5y-15=-15$

   $⇒y(x+5)-3(x+5)=-15$

   $⇒(x+5)(y-3)=-15$

   TH1,2:

   $\left[ \begin{array}{l}\left \{ {{x+5=-5} \atop {y-3=3}} \right.\\\left \{ {{x+5=5} \atop {y-3=-3}} \right.\end{array} \right.$ 

   $⇒\left[ \begin{array}{l}\left \{ {{x=-10} \atop {y=6}} \right.\\\left \{ {{x=0} \atop {y=0}} \right.\end{array} \right.$ 

   TH3,4:

   $\left[ \begin{array}{l}\left \{ {{x+5=-1} \atop {y-3=15}} \right.\\\left \{ {{x+5=1} \atop {y-3=15}} \right.\end{array} \right.$ 

   $⇒\left[ \begin{array}{l}\left \{ {{x=-6} \atop {y=18}} \right.\\\left \{ {{x=-4} \atop {y=18}} \right.\end{array} \right.$ 

   TH5,6:

   $\left[ \begin{array}{l}\left \{ {{x+5=-3} \atop {y-3=5}} \right.\\\left \{ {{x+5=3} \atop {y-3=-5}} \right.\end{array} \right.$ 

   $⇒\left[ \begin{array}{l}\left \{ {{x=-8} \atop {y=8}} \right.\\\left \{ {{x=-2} \atop {y-2}} \right.\end{array} \right.$ 

   TH6,7: 

   $\left[ \begin{array}{l}\left \{ {{x+5=-15} \atop {y-3=1}} \right.\\\left \{ {{x+5=15} \atop {y-3=-1}} \right.\end{array} \right.$ 

   $⇒\left[ \begin{array}{l}\left \{ {{x=-20} \atop {y=4}} \right.\\\left \{ {{x=10} \atop {y=-2}} \right.\end{array} \right.$ 

   Vậy $(x;y)=……….$

    

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