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人気のある代数 >

x^{10}+x^5+1=0

解

x^{10} + x^{5} + 1 = 0

解

x = cos (\frac{2 π}{15}) + i sin (\frac{2 π}{15}), x = cos (\frac{8 π}{15}) + i sin (\frac{8 π}{15}), x = cos (\frac{14 π}{15}) + i sin (\frac{14 π}{15}), x = - \frac{1}{2} - i \frac{3}{2}, x = cos (\frac{26 π}{15}) + i sin (\frac{26 π}{15}), x = cos (\frac{2 π}{15}) - i sin (\frac{2 π}{15}), x = cos (\frac{4 π}{15}) + i sin (\frac{4 π}{15}), x = - \frac{1}{2} + i \frac{3}{2}, x = cos (\frac{16 π}{15}) + i sin (\frac{16 π}{15}), x = cos (\frac{22 π}{15}) + i sin (\frac{22 π}{15})

解答ステップ

x^{10} + x^{5} + 1 = 0

equationを

u = x^{5}

と以下で書き換える:

u^{2} = x^{10}

u^{2} + u + 1 = 0

解く

u^{2} + u + 1 = 0 : u = - \frac{1}{2} + i \frac{3}{2}, u = - \frac{1}{2} - i \frac{3}{2}

u = - \frac{1}{2} + i \frac{3}{2}, u = - \frac{1}{2} - i \frac{3}{2}

再び

u = x^{5}

に置き換えて以下を解く:

x

解く

x^{5} = - \frac{1}{2} + i \frac{3}{2} : x = cos (\frac{2 π}{15}) + i sin (\frac{2 π}{15}), x = cos (\frac{8 π}{15}) + i sin (\frac{8 π}{15}), x = cos (\frac{14 π}{15}) + i sin (\frac{14 π}{15}), x = - \frac{1}{2} - i \frac{3}{2}, x = cos (\frac{26 π}{15}) + i sin (\frac{26 π}{15})

解く

x^{5} = - \frac{1}{2} - i \frac{3}{2} : x = cos (\frac{2 π}{15}) - i sin (\frac{2 π}{15}), x = cos (\frac{4 π}{15}) + i sin (\frac{4 π}{15}), x = - \frac{1}{2} + i \frac{3}{2}, x = cos (\frac{16 π}{15}) + i sin (\frac{16 π}{15}), x = cos (\frac{22 π}{15}) + i sin (\frac{22 π}{15})

解答は

x = cos (\frac{2 π}{15}) + i sin (\frac{2 π}{15}), x = cos (\frac{8 π}{15}) + i sin (\frac{8 π}{15}), x = cos (\frac{14 π}{15}) + i sin (\frac{14 π}{15}), x = - \frac{1}{2} - i \frac{3}{2}, x = cos (\frac{26 π}{15}) + i sin (\frac{26 π}{15}), x = cos (\frac{2 π}{15}) - i sin (\frac{2 π}{15}), x = cos (\frac{4 π}{15}) + i sin (\frac{4 π}{15}), x = - \frac{1}{2} + i \frac{3}{2}, x = cos (\frac{16 π}{15}) + i sin (\frac{16 π}{15}), x = cos (\frac{22 π}{15}) + i sin (\frac{22 π}{15})

グラフ

人気の例

y^3-25y^2-178y+1165=0

y^{3} - 25 y^{2} - 178 y + 1165 = 0

x^{4} - 3 = 2 x + 1

solvefor x,g=r(x+q)^7+s

so l v e f or x, g = r (x + q)^{7} + s

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