解
解く y,(x+x2+1)(y+y2+1)=1
解
y=x{x=0},y=−x
解答ステップ
(x+x2+1)(y+y2+1)=1
拡張 (x+x2+1)(y+y2+1):yx+y2+1x+yx2+1+y2+1x2+1
yx+y2+1x+yx2+1+y2+1x2+1=1
因数 yx+y2+1x+yx2+1+y2+1x2+1:(x2+1+x)(y+y2+1)
(x2+1+x)(y+y2+1)=1
両辺を2乗する:4y2x2+4y2xx2+1+2y2+4yx2y2+1+4yxy2+1x2+1+2yy2+1+2x2+2xx2+1+1=1
4y2x2+4y2xx2+1+2y2+4yx2y2+1+4yxy2+1x2+1+2yy2+1+2x2+2xx2+1+1=1
両辺から1を引く4y2x2+4y2xx2+1+2y2+4yx2y2+1+4yxy2+1x2+1+2yy2+1+2x2+2xx2+1+1−1=1−1
簡素化4y2x2+4y2xx2+1+2y2+4yx2y2+1+4yxy2+1x2+1+2yy2+1+2x2+2xx2+1=0
4y2x2を右側に移動します
4y2xx2+1+2y2+4yx2y2+1+4yxy2+1x2+1+2yy2+1+2x2+2xx2+1=−4x2y2
4y2xx2+1を右側に移動します
2y2+4yx2y2+1+4yxy2+1x2+1+2yy2+1+2x2+2xx2+1=−4x2y2−4y2xx2+1
2y2を右側に移動します
4yx2y2+1+4yxy2+1x2+1+2yy2+1+2x2+2xx2+1=−4x2y2−4y2xx2+1−2y2
2x2を右側に移動します
4yx2y2+1+4yxy2+1x2+1+2yy2+1+2xx2+1=−4x2y2−4y2xx2+1−2y2−2x2
2xx2+1を右側に移動します
4yx2y2+1+4yxy2+1x2+1+2yy2+1=−4x2y2−4y2xx2+1−2y2−2x2−2xx2+1
両辺から−4x2y2−4y2xx2+1−2y2−2x2−2xx2+1を引く4yx2y2+1+4yxy2+1x2+1+2yy2+1−(−4x2y2−4y2xx2+1−2y2−2x2−2xx2+1)=−4x2y2−4y2xx2+1−2y2−2x2−2xx2+1−(−4x2y2−4y2xx2+1−2y2−2x2−2xx2+1)
簡素化4x2yy2+1+4xyy2+1x2+1+2yy2+1+4x2y2+4xy2x2+1+2y2+2x2+2xx2+1=0
因数 4x2yy2+1+4xyy2+1x2+1+2yy2+1+4x2y2+4xy2x2+1+2y2+2x2+2xx2+1:2(2x2yy2+1+2xyy2+1x2+1+yy2+1+2x2y2+2xy2x2+1+y2+x2+xx2+1)
2(2x2yy2+1+2xyy2+1x2+1+yy2+1+2x2y2+2xy2x2+1+y2+x2+xx2+1)=0
以下で両辺を割る2
2x2yy2+1+2xyy2+1x2+1+yy2+1+2x2y2+2xy2x2+1+y2+x2+xx2+1=0
2x2y2を右側に移動します
2x2yy2+1+2xyy2+1x2+1+yy2+1+2xy2x2+1+y2+x2+xx2+1=−2x2y2
2xy2x2+1を右側に移動します
2x2yy2+1+2xyy2+1x2+1+yy2+1+y2+x2+xx2+1=−2x2y2−2xy2x2+1
y2を右側に移動します
2x2yy2+1+2xyy2+1x2+1+yy2+1+x2+xx2+1=−2x2y2−2xy2x2+1−y2
x2を右側に移動します
2x2yy2+1+2xyy2+1x2+1+yy2+1+xx2+1=−2x2y2−2xy2x2+1−y2−x2
xx2+1を右側に移動します
2x2yy2+1+2xyy2+1x2+1+yy2+1=−2x2y2−2xy2x2+1−y2−x2−xx2+1
因数 2x2yy2+1+2xyy2+1x2+1+yy2+1:yy2+1(2x2+2xx2+1+1)
yy2+1(2x2+2xx2+1+1)=−2x2y2−2xy2x2+1−y2−x2−xx2+1
以下で両辺を割るy(2x2+2xx2+1+1)
y2+1=y(1+2x2+2xx2+1)−2x2y2−2xy2x2+1−y2−x2−xx2+1
両辺を2乗する:y2+1=8y2x4+8y2x2+4y2xx2+1+8y2x3x2+1+y28y4x4+8y2x4+2x4+8y4x3x2+1+8y2x3x2+1+2x3x2+1+8y4x2+6y2x2+x2+4y4xx2+1+2y2xx2+1+y4
y2+1=8y2x4+8y2x2+4y2xx2+1+8y2x3x2+1+y28y4x4+8y2x4+2x4+8y4x3x2+1+8y2x3x2+1+2x3x2+1+8y4x2+6y2x2+x2+4y4xx2+1+2y2xx2+1+y4
解く y2+1=8y2x4+8y2x2+4y2xx2+1+8y2x3x2+1+y28y4x4+8y2x4+2x4+8y4x3x2+1+8y2x3x2+1+2x3x2+1+8y4x2+6y2x2+x2+4y4xx2+1+2y2xx2+1+y4:y=x,y=−x
y=x,y=−x
解を検算する:y=x{x=0},y=−x真
解答はy=x{x=0},y=−x