Question

Rezolvați in multimea numerelor intregi ecuatia x la puterea 2 +xy= 2y+203.

Answer 1

x² +xy= 2y+203

x²+xy-2y-4=199

(x-2)(x+2)+y(x-2)=199

(x-2)(x+2+y)=199

(x-2)=1  si (x+2+y)= 199

=> x=3 si y=199-5=194

(x-2)=199  si (x+2+y)=1

=> x=201 si y=1-203=-202

(x-2)=-1  si (x+2+y)= -199

=> x=1  si y=-199-3=-202

(x-2)=-199  si (x+2+y)= -1

=> x=-197 si y=-1+195=194