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人気のある代数 >

solvefor y,(x^2+y^2+ax)^2=a^2(x^2+y^2)

解

解く

y, (x^{2} + y^{2} + a x)^{2} = a^{2} (x^{2} + y^{2})

解

y = \frac{- 2 x ^{2} - 2 a x + a ^{2} + - 4 a ^{3} x + a ^{4}}{2}, y = - \frac{- 2 x ^{2} - 2 a x + a ^{2} + - 4 a ^{3} x + a ^{4}}{2}, y = \frac{- 2 x ^{2} - 2 a x + a ^{2} - - 4 a ^{3} x + a ^{4}}{2}, y = - \frac{- 2 x ^{2} - 2 a x + a ^{2} - - 4 a ^{3} x + a ^{4}}{2}

解答ステップ

(x^{2} + y^{2} + a x)^{2} = a^{2} (x^{2} + y^{2})

拡張

(x^{2} + y^{2} + a x)^{2} : 2 a x^{3} + 2 y^{2} x^{2} + x^{4} + a^{2} x^{2} + 2 a y^{2} x + y^{4}

拡張

a^{2} (x^{2} + y^{2}) : a^{2} x^{2} + a^{2} y^{2}

2 a x^{3} + 2 y^{2} x^{2} + x^{4} + a^{2} x^{2} + 2 a y^{2} x + y^{4} = a^{2} x^{2} + a^{2} y^{2}

両辺から

a^{2} x^{2} + a^{2} y^{2}

を引く

2 a x^{3} + 2 y^{2} x^{2} + x^{4} + a^{2} x^{2} + 2 a y^{2} x + y^{4} - (a^{2} x^{2} + a^{2} y^{2}) = a^{2} x^{2} + a^{2} y^{2} - (a^{2} x^{2} + a^{2} y^{2})

簡素化

y^{4} + (2 x^{2} + 2 a x - a^{2}) y^{2} + x^{4} + 2 a x^{3} = 0

equationを

u = y^{2}

と以下で書き換える:

u^{2} = y^{4}

u^{2} + (2 x^{2} + 2 a x - a^{2}) u + x^{4} + 2 a x^{3} = 0

解く

u^{2} + (2 x^{2} + 2 a x - a^{2}) u + x^{4} + 2 a x^{3} = 0 : u = \frac{- 2 x ^{2} - 2 a x + a ^{2} + - 4 a ^{3} x + a ^{4}}{2}, u = \frac{- 2 x ^{2} - 2 a x + a ^{2} - - 4 a ^{3} x + a ^{4}}{2}

u = \frac{- 2 x ^{2} - 2 a x + a ^{2} + - 4 a ^{3} x + a ^{4}}{2}, u = \frac{- 2 x ^{2} - 2 a x + a ^{2} - - 4 a ^{3} x + a ^{4}}{2}

再び

u = y^{2}

に置き換えて以下を解く:

y

解く

y^{2} = \frac{- 2 x ^{2} - 2 a x + a ^{2} + - 4 a ^{3} x + a ^{4}}{2} : y = \frac{- 2 x ^{2} - 2 a x + a ^{2} + - 4 a ^{3} x + a ^{4}}{2}, y = - \frac{- 2 x ^{2} - 2 a x + a ^{2} + - 4 a ^{3} x + a ^{4}}{2}

解く

y^{2} = \frac{- 2 x ^{2} - 2 a x + a ^{2} - - 4 a ^{3} x + a ^{4}}{2} : y = \frac{- 2 x ^{2} - 2 a x + a ^{2} - - 4 a ^{3} x + a ^{4}}{2}, y = - \frac{- 2 x ^{2} - 2 a x + a ^{2} - - 4 a ^{3} x + a ^{4}}{2}

解答は

y = \frac{- 2 x ^{2} - 2 a x + a ^{2} + - 4 a ^{3} x + a ^{4}}{2}, y = - \frac{- 2 x ^{2} - 2 a x + a ^{2} + - 4 a ^{3} x + a ^{4}}{2}, y = \frac{- 2 x ^{2} - 2 a x + a ^{2} - - 4 a ^{3} x + a ^{4}}{2}, y = - \frac{- 2 x ^{2} - 2 a x + a ^{2} - - 4 a ^{3} x + a ^{4}}{2}

グラフ

人気の例

x^{3} + 24 x + 16 = 0

x^3=38+17sqrt(5)

x^{3} = 38 + 175

(2 x^{2} - 4)^{2} + 9 = 0

1 - (4 - 3 x)^{3} = 9

16x^4-40x^2+9=0

16 x^{4} - 40 x^{2} + 9 = 0