x2+2x2y2+2y2−(x2y2+2x2)−2=0x2+2x2y2+2y2−(x2y2+2x2)−2=0
⇔x2+2x2y2+2y2−x2y2−2x2−2=0⇔x2+2x2y2+2y2−x2y2−2x2−2=0
⇔x2y2−x2+2y2−2=0⇔x2y2−x2+2y2−2=0
⇔(x2y2−x2)+(2y2−2)=0⇔(x2y2−x2)+(2y2−2)=0
⇔x2(y2−1)+2(y2−1)=0⇔x2(y2−1)+2(y2−1)=0
⇔(x2+2)(y2−1)=0⇔(x2+2)(y2−1)=0
⇔(x2+2)(y−1)(y+1)=0⇔(x2+2)(y−1)(y+1)=0
Dễ thấy: x2+2≥2>0∀xx2+2≥2>0∀x (vô nghiệm)
⇒[y−1=0y+1=0⇒[y−1=0y+1=0⇒[y=1y=−1