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人気のある代数 >

solvefor x,x^4x^2-9y^2=36

解

解く

x, x^{4} x^{2} - 9 y^{2} = 36

解

x = 3 36 + 9 y^{2}, x = - 3 36 + 9 y^{2}

解答ステップ

x^{4} x^{2} - 9 y^{2} = 36

9 y^{2}

を右側に移動します

x^{4} x^{2} = 36 + 9 y^{2}

簡素化

x^{6} = 36 + 9 y^{2}

equationを

u = x^{2}

と以下で書き換える:

u^{3} = x^{6}

u^{3} = 36 + 9 y^{2}

解く

u^{3} = 36 + 9 y^{2} : u = 3 36 + 9 y^{2}, u = 3 36 + 9 y^{2} \frac{- 1 + 3 i}{2}, u = 3 36 + 9 y^{2} \frac{- 1 - 3 i}{2}

u = 3 36 + 9 y^{2}, u = 3 36 + 9 y^{2} \frac{- 1 + 3 i}{2}, u = 3 36 + 9 y^{2} \frac{- 1 - 3 i}{2}

再び

u = x^{2}

に置き換えて以下を解く:

x

解く

x^{2} = 3 36 + 9 y^{2} : x = 3 36 + 9 y^{2}, x = - 3 36 + 9 y^{2}

解く

x^{2} = 3 36 + 9 y^{2} \frac{- 1 + 3 i}{2} :

解なし

解く

x^{2} = 3 36 + 9 y^{2} \frac{- 1 - 3 i}{2} :

解なし

解答は

x = 3 36 + 9 y^{2}, x = - 3 36 + 9 y^{2}

グラフ

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