(x,y)={(−1;−2);(1;2);(2;1);(−2;−1)}(x,y)={(−1;−2);(1;2);(2;1);(−2;−1)}
Giải thích các bước giải:
{x2+y2+xy=7x4+y4+x2y2=21⇔{x2+y2+xy=7(x2+y2)2−x2y2=21{x2+y2+xy=7x4+y4+x2y2=21⇔{x2+y2+xy=7(x2+y2)2−x2y2=21
Đặt (x2+y2)=u(x2+y2)=u; x.y=vx.y=v
Ta được hệ phương trình:
{u+v=7u2−v2=21⇔{u+v=7(u+v)(u−v)=21⇔{u+v=7u−v=3{u+v=7u2−v2=21⇔{u+v=7(u+v)(u−v)=21⇔{u+v=7u−v=3
⇔{u=5v=2⇔{x2+y2=5x.y=2⇔{x2+y2−2xy=1xy=2⇔{u=5v=2⇔{x2+y2=5x.y=2⇔{x2+y2−2xy=1xy=2
⇔{(x−y)2=1xy=2⇔{|x−y|=1xy=2⇔{x−y=1 hoặc x−y=−1xy=2⇔{(x−y)2=1xy=2⇔{|x−y|=1xy=2⇔{x−y=1 hoặc x−y=−1xy=2
Th1:
{x−y=1xy=2{x−y=1xy=2
⇔(y+1)y=2⇔(y+1)y=2
⇔y2+y−2=0⇔y2+y−2=0
⇔(y−1)(y+2)=0⇔(y−1)(y+2)=0
⇔[y=1⇒x=2y=−2⇒x=−1⇔[y=1⇒x=2y=−2⇒x=−1
TH2:
{x−y=−1xy=2{x−y=−1xy=2
⇔(y−1)y=2⇔y2−y−2=0⇔(y−1)y=2⇔y2−y−2=0
⇔(y+1)(y−2)=0⇔(y+1)(y−2)=0
⇔[y=−1⇒x=−2y=2⇒x=1
