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Question Number 63945 by mathmax by abdo last updated on 11/Jul/19

solve at Z^2 x^2 −2y^2 +xy +2 =0

solveatZ2x2−2y2+xy+2=0

Commented by hknkrc46 last updated on 11/Jul/19

x^2 −2y^2 +xy+2=(x^2 −y^2 )+(xy−y^2 )+2=0 (x−y)(x+y)+y(x−y)+2=0 (x−y)(x+y+y)+2=0 (x−y)(x+2y)+2=0 1) x−y=1∧x+2y=−2⇒(x,y)=(0,−1) 2) x−y=−1∧x+2y=2⇒(x,y)=(0,1) 3) x−y=2∧x+2y=−1⇒(x,y)=(1,−1) 4) x−y=−2∧x+2y=1⇒(x,y)=(−1,1)

x2−2y2+xy+2=(x2−y2)+(xy−y2)+2=0(x−y)(x+y)+y(x−y)+2=0(x−y)(x+y+y)+2=0(x−y)(x+2y)+2=01)x−y=1∧x+2y=−2⇒(x,y)=(0,−1)2)x−y=−1∧x+2y=2⇒(x,y)=(0,1)3)x−y=2∧x+2y=−1⇒(x,y)=(1,−1)4)x−y=−2∧x+2y=1⇒(x,y)=(−1,1)

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