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人気のある代数 >

solvefor z,z^2(p^2z^2+q^2)=1

解

解く

z, z^{2} (p^{2} z^{2} + q^{2}) = 1

解

z = \frac{- q ^{2} + q ^{4} + 4 p ^{2}}{2 p}, z = - \frac{- q ^{2} + q ^{4} + 4 p ^{2}}{2 p}, z = \frac{- q ^{2} - q ^{4} + 4 p ^{2}}{2 p}, z = - \frac{- q ^{2} - q ^{4} + 4 p ^{2}}{2 p}

解答ステップ

z^{2} (p^{2} z^{2} + q^{2}) = 1

拡張

z^{2} (p^{2} z^{2} + q^{2}) : z^{4} p^{2} + z^{2} q^{2}

z^{4} p^{2} + z^{2} q^{2} = 1

1

を左側に移動します

z^{4} p^{2} + z^{2} q^{2} - 1 = 0

標準的な形式で書く

a_{n} x^{n} + \dots + q x + p = 0

p^{2} z^{4} + q^{2} z^{2} - 1 = 0

equationを

u = z^{2}

と以下で書き換える:

u^{2} = z^{4}

p^{2} u^{2} + q^{2} u - 1 = 0

解く

p^{2} u^{2} + q^{2} u - 1 = 0 : u = \frac{- q ^{2} + q ^{4} + 4 p ^{2}}{2 p ^{2}}, u = \frac{- q ^{2} - q ^{4} + 4 p ^{2}}{2 p ^{2}}; p \neq = 0

u = \frac{- q ^{2} + q ^{4} + 4 p ^{2}}{2 p ^{2}}, u = \frac{- q ^{2} - q ^{4} + 4 p ^{2}}{2 p ^{2}}; p \neq = 0

再び

u = z^{2}

に置き換えて以下を解く:

z

解く

z^{2} = \frac{- q ^{2} + q ^{4} + 4 p ^{2}}{2 p ^{2}} : z = \frac{- q ^{2} + q ^{4} + 4 p ^{2}}{2 p}, z = - \frac{- q ^{2} + q ^{4} + 4 p ^{2}}{2 p}

解く

z^{2} = \frac{- q ^{2} - q ^{4} + 4 p ^{2}}{2 p ^{2}} : z = \frac{- q ^{2} - q ^{4} + 4 p ^{2}}{2 p}, z = - \frac{- q ^{2} - q ^{4} + 4 p ^{2}}{2 p}

解答は

z = \frac{- q ^{2} + q ^{4} + 4 p ^{2}}{2 p}, z = - \frac{- q ^{2} + q ^{4} + 4 p ^{2}}{2 p}, z = \frac{- q ^{2} - q ^{4} + 4 p ^{2}}{2 p}, z = - \frac{- q ^{2} - q ^{4} + 4 p ^{2}}{2 p}

グラフ

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