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人気のある代数 >

(1+x^2)^2=4(1-x^2)

解

(1 + x^{2})^{2} = 4 (1 - x^{2})

解

x = - 3 + 23, x = - - 3 + 23, x = 3 + 23 i, x = - 3 + 23 i

解答ステップ

(1 + x^{2})^{2} = 4 (1 - x^{2})

拡張

(1 + x^{2})^{2} : 1 + 2 x^{2} + x^{4}

拡張

4 (1 - x^{2}) : 4 - 4 x^{2}

1 + 2 x^{2} + x^{4} = 4 - 4 x^{2}

4 x^{2}

を左側に移動します

x^{4} + 6 x^{2} + 1 = 4

4

を左側に移動します

x^{4} + 6 x^{2} - 3 = 0

equationを

u = x^{2}

と以下で書き換える:

u^{2} = x^{4}

u^{2} + 6 u - 3 = 0

解く

u^{2} + 6 u - 3 = 0 : u = - 3 + 23, u = - 3 - 23

u = - 3 + 23, u = - 3 - 23

再び

u = x^{2}

に置き換えて以下を解く:

x

解く

x^{2} = - 3 + 23 : x = - 3 + 23, x = - - 3 + 23

解く

x^{2} = - 3 - 23 : x = 3 + 23 i, x = - 3 + 23 i

解答は

x = - 3 + 23, x = - - 3 + 23, x = 3 + 23 i, x = - 3 + 23 i

グラフ

人気の例

x^{3} + 6 = 12

x^{4} + 5 x^{2} - 50 = 0

128 x^{3} - 16 x = 0

x^{4} + a^{2} = 0

4 x^{4} + 2 x^{2} - 56 = 0