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人気のある代数 >

x^2+x^{10}=0

解

x^{2} + x^{10} = 0

解

x = 0, x = \frac{- 1 + 2}{4 2 ^{3}} + \frac{1}{2 ^{\frac{3}{4}} - 1 + 2} i, x = - \frac{- 1 + 2}{4 2 ^{3}} - \frac{1}{2 ^{\frac{3}{4}} - 1 + 2} i, x = \frac{- 1 + 2}{4 2 ^{3}} - \frac{1}{2 ^{\frac{3}{4}} - 1 + 2} i, x = - \frac{- 1 + 2}{4 2 ^{3}} + \frac{1}{2 ^{\frac{3}{4}} - 1 + 2} i, x = \frac{1 + 2}{4 2 ^{3}} + \frac{1}{2 ^{\frac{3}{4}} 1 + 2} i, x = - \frac{1 + 2}{4 2 ^{3}} - \frac{1}{2 ^{\frac{3}{4}} 1 + 2} i, x = \frac{1 + 2}{4 2 ^{3}} - \frac{1}{2 ^{\frac{3}{4}} 1 + 2} i, x = - \frac{1 + 2}{4 2 ^{3}} + \frac{1}{2 ^{\frac{3}{4}} 1 + 2} i

解答ステップ

x^{2} + x^{10} = 0

標準的な形式で書く

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

x^{10} + x^{2} = 0

equationを

u = x^{2}

と以下で書き換える:

u^{5} = x^{10}

u^{5} + u = 0

解く

u^{5} + u = 0 : u = 0, u = - \frac{2}{2} + i \frac{2}{2}, u = - \frac{2}{2} - i \frac{2}{2}, u = \frac{2}{2} + i \frac{2}{2}, u = \frac{2}{2} - i \frac{2}{2}

u = 0, u = - \frac{2}{2} + i \frac{2}{2}, u = - \frac{2}{2} - i \frac{2}{2}, u = \frac{2}{2} + i \frac{2}{2}, u = \frac{2}{2} - i \frac{2}{2}

再び

u = x^{2}

に置き換えて以下を解く:

x

解く

x^{2} = 0 : x = 0

解く

x^{2} = - \frac{2}{2} + i \frac{2}{2} : x = \frac{- 1 + 2}{4 2 ^{3}} + \frac{1}{2 ^{\frac{3}{4}} - 1 + 2} i, x = - \frac{- 1 + 2}{4 2 ^{3}} - \frac{1}{2 ^{\frac{3}{4}} - 1 + 2} i

解く

x^{2} = - \frac{2}{2} - i \frac{2}{2} : x = \frac{- 1 + 2}{4 2 ^{3}} - \frac{1}{2 ^{\frac{3}{4}} - 1 + 2} i, x = - \frac{- 1 + 2}{4 2 ^{3}} + \frac{1}{2 ^{\frac{3}{4}} - 1 + 2} i

解く

x^{2} = \frac{2}{2} + i \frac{2}{2} : x = \frac{1 + 2}{4 2 ^{3}} + \frac{1}{2 ^{\frac{3}{4}} 1 + 2} i, x = - \frac{1 + 2}{4 2 ^{3}} - \frac{1}{2 ^{\frac{3}{4}} 1 + 2} i

解く

x^{2} = \frac{2}{2} - i \frac{2}{2} : x = \frac{1 + 2}{4 2 ^{3}} - \frac{1}{2 ^{\frac{3}{4}} 1 + 2} i, x = - \frac{1 + 2}{4 2 ^{3}} + \frac{1}{2 ^{\frac{3}{4}} 1 + 2} i

解答は

x = 0, x = \frac{- 1 + 2}{4 2 ^{3}} + \frac{1}{2 ^{\frac{3}{4}} - 1 + 2} i, x = - \frac{- 1 + 2}{4 2 ^{3}} - \frac{1}{2 ^{\frac{3}{4}} - 1 + 2} i, x = \frac{- 1 + 2}{4 2 ^{3}} - \frac{1}{2 ^{\frac{3}{4}} - 1 + 2} i, x = - \frac{- 1 + 2}{4 2 ^{3}} + \frac{1}{2 ^{\frac{3}{4}} - 1 + 2} i, x = \frac{1 + 2}{4 2 ^{3}} + \frac{1}{2 ^{\frac{3}{4}} 1 + 2} i, x = - \frac{1 + 2}{4 2 ^{3}} - \frac{1}{2 ^{\frac{3}{4}} 1 + 2} i, x = \frac{1 + 2}{4 2 ^{3}} - \frac{1}{2 ^{\frac{3}{4}} 1 + 2} i, x = - \frac{1 + 2}{4 2 ^{3}} + \frac{1}{2 ^{\frac{3}{4}} 1 + 2} i

グラフ

人気の例

4 \cdot x^{3} = 32

solvefor x,xx^2+y^2=0

so l v e f or x, x x^{2} + y^{2} = 0

r^{3} = 6

1 x^{5} = 5

(x - 2)^{4} = 16