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人気のある代数 >

2a^2(a^2+2)=27+7a^2

解

2 a^{2} (a^{2} + 2) = 27 + 7 a^{2}

解

a = \frac{3}{2}, a = - \frac{3}{2}, a = 3 i, a = - 3 i

解答ステップ

2 a^{2} (a^{2} + 2) = 27 + 7 a^{2}

拡張

2 a^{2} (a^{2} + 2) : 2 a^{4} + 4 a^{2}

2 a^{4} + 4 a^{2} = 27 + 7 a^{2}

7 a^{2}

を左側に移動します

2 a^{4} - 3 a^{2} = 27

27

を左側に移動します

2 a^{4} - 3 a^{2} - 27 = 0

equationを

u = a^{2}

と以下で書き換える:

u^{2} = a^{4}

2 u^{2} - 3 u - 27 = 0

解く

2 u^{2} - 3 u - 27 = 0 : u = \frac{9}{2}, u = - 3

u = \frac{9}{2}, u = - 3

再び

u = a^{2}

に置き換えて以下を解く:

a

解く

a^{2} = \frac{9}{2} : a = \frac{3}{2}, a = - \frac{3}{2}

解く

a^{2} = - 3 : a = 3 i, a = - 3 i

解答は

a = \frac{3}{2}, a = - \frac{3}{2}, a = 3 i, a = - 3 i

グラフ

人気の例

2 x - 53 = 2 + x^{15}

4 x^{3} = 256 x

2 x^{4} + 8 x^{2} + 5 = 0

solvefor a,a^3+b^3=8

so l v e f or a, a^{3} + b^{3} = 8

x^3+27+x^2-6x-27=0

x^{3} + 27 + x^{2} - 6 x - 27 = 0