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人気のある代数 >

64a^6-112a^4+56a^2-7=0

解

64 a^{6} - 112 a^{4} + 56 a^{2} - 7 = 0

解

a = \frac{2.35319 E 15}{1.25 E 16}, a = - \frac{2.35319 E 15}{1.25 E 16}, a = \frac{3.0563 E 15}{5.0 E 15}, a = - \frac{3.0563 E 15}{5.0 E 15}, a = \frac{2.97026 E 14}{3.125 E 14}, a = - \frac{2.97026 E 14}{3.125 E 14}

+1

十進法表記

a = 0.43388 \dots, a = - 0.43388 \dots, a = 0.78183 \dots, a = - 0.78183 \dots, a = 0.97492 \dots, a = - 0.97492 \dots

解答ステップ

64 a^{6} - 112 a^{4} + 56 a^{2} - 7 = 0

equationを

u = a^{2}, u^{2} = a^{4}

と以下で書き換える:

u^{3} = a^{6}

64 u^{3} - 112 u^{2} + 56 u - 7 = 0

解く

64 u^{3} - 112 u^{2} + 56 u - 7 = 0 : u \approx 0.18825 \dots, u \approx 0.61126 \dots, u \approx 0.95048 \dots

u \approx 0.18825 \dots, u \approx 0.61126 \dots, u \approx 0.95048 \dots

再び

u = a^{2}

に置き換えて以下を解く:

a

解く

a^{2} = 0.18825 \dots : a = \frac{2.35319 E 15}{1.25 E 16}, a = - \frac{2.35319 E 15}{1.25 E 16}

解く

a^{2} = 0.61126 \dots : a = \frac{3.0563 E 15}{5.0 E 15}, a = - \frac{3.0563 E 15}{5.0 E 15}

解く

a^{2} = 0.95048 \dots : a = \frac{2.97026 E 14}{3.125 E 14}, a = - \frac{2.97026 E 14}{3.125 E 14}

解答は

a = \frac{2.35319 E 15}{1.25 E 16}, a = - \frac{2.35319 E 15}{1.25 E 16}, a = \frac{3.0563 E 15}{5.0 E 15}, a = - \frac{3.0563 E 15}{5.0 E 15}, a = \frac{2.97026 E 14}{3.125 E 14}, a = - \frac{2.97026 E 14}{3.125 E 14}

グラフ

人気の例

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x^{1} + 2 x^{2} + x^{3} = - 1

4x^3-54x^2+180x-125=0

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b^4-6b^3-5b^2+42b+40=0

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