ja

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

人気のある代数 >

x^9+n^5-n^4-1=0

解

x^{9} + n^{5} - n^{4} - 1 = 0

解

x = 3 3 - n^{5} + n^{4} + 1, x = - \frac{3 3 - n ^{5} + n ^{4} + 1}{2} + \frac{3 3 - n ^{5} + n ^{4} + 1 3}{2} i, x = - \frac{3 3 - n ^{5} + n ^{4} + 1}{2} - \frac{3 3 - n ^{5} + n ^{4} + 1 3}{2} i, x = cos (\frac{π}{9}) 6 (1 + n^{4} - n^{5})^{\frac{2}{3}} - i sin (\frac{π}{9}) 6 (1 + n^{4} - n^{5})^{\frac{2}{3}}, x = cos (\frac{5 π}{9}) 6 (1 + n^{4} - n^{5})^{\frac{2}{3}} + i sin (\frac{5 π}{9}) 6 (1 + n^{4} - n^{5})^{\frac{2}{3}}, x = cos (\frac{11 π}{9}) 6 (1 + n^{4} - n^{5})^{\frac{2}{3}} + i sin (\frac{11 π}{9}) 6 (1 + n^{4} - n^{5})^{\frac{2}{3}}, x = cos (\frac{π}{9}) 6 (1 + n^{4} - n^{5})^{\frac{2}{3}} + i sin (\frac{π}{9}) 6 (1 + n^{4} - n^{5})^{\frac{2}{3}}, x = cos (\frac{7 π}{9}) 6 (1 + n^{4} - n^{5})^{\frac{2}{3}} + i sin (\frac{7 π}{9}) 6 (1 + n^{4} - n^{5})^{\frac{2}{3}}, x = cos (\frac{13 π}{9}) 6 (1 + n^{4} - n^{5})^{\frac{2}{3}} + i sin (\frac{13 π}{9}) 6 (1 + n^{4} - n^{5})^{\frac{2}{3}}

解答ステップ

x^{9} + n^{5} - n^{4} - 1 = 0

n^{5}

を右側に移動します

x^{9} - n^{4} - 1 = - n^{5}

n^{4}

を右側に移動します

x^{9} - 1 = - n^{5} + n^{4}

1

を右側に移動します

x^{9} = - n^{5} + n^{4} + 1

equationを

u = x^{3}

と以下で書き換える:

u^{3} = x^{9}

u^{3} = - n^{5} + n^{4} + 1

解く

u^{3} = - n^{5} + n^{4} + 1 : u = 3 - n^{5} + n^{4} + 1, u = 3 - n^{5} + n^{4} + 1 \frac{- 1 + 3 i}{2}, u = 3 - n^{5} + n^{4} + 1 \frac{- 1 - 3 i}{2}

u = 3 - n^{5} + n^{4} + 1, u = 3 - n^{5} + n^{4} + 1 \frac{- 1 + 3 i}{2}, u = 3 - n^{5} + n^{4} + 1 \frac{- 1 - 3 i}{2}

再び

u = x^{3}

に置き換えて以下を解く:

x

解く

x^{3} = 3 - n^{5} + n^{4} + 1 : x = 3 3 - n^{5} + n^{4} + 1, x = - \frac{3 3 - n ^{5} + n ^{4} + 1}{2} + \frac{3 3 - n ^{5} + n ^{4} + 1 3}{2} i, x = - \frac{3 3 - n ^{5} + n ^{4} + 1}{2} - \frac{3 3 - n ^{5} + n ^{4} + 1 3}{2} i

解く

x^{3} = 3 - n^{5} + n^{4} + 1 \frac{- 1 + 3 i}{2} : x = cos (\frac{π}{9}) 6 (1 + n^{4} - n^{5})^{\frac{2}{3}} - i sin (\frac{π}{9}) 6 (1 + n^{4} - n^{5})^{\frac{2}{3}}, x = cos (\frac{5 π}{9}) 6 (1 + n^{4} - n^{5})^{\frac{2}{3}} + i sin (\frac{5 π}{9}) 6 (1 + n^{4} - n^{5})^{\frac{2}{3}}, x = cos (\frac{11 π}{9}) 6 (1 + n^{4} - n^{5})^{\frac{2}{3}} + i sin (\frac{11 π}{9}) 6 (1 + n^{4} - n^{5})^{\frac{2}{3}}

解く

x^{3} = 3 - n^{5} + n^{4} + 1 \frac{- 1 - 3 i}{2} : x = cos (\frac{π}{9}) 6 (1 + n^{4} - n^{5})^{\frac{2}{3}} + i sin (\frac{π}{9}) 6 (1 + n^{4} - n^{5})^{\frac{2}{3}}, x = cos (\frac{7 π}{9}) 6 (1 + n^{4} - n^{5})^{\frac{2}{3}} + i sin (\frac{7 π}{9}) 6 (1 + n^{4} - n^{5})^{\frac{2}{3}}, x = cos (\frac{13 π}{9}) 6 (1 + n^{4} - n^{5})^{\frac{2}{3}} + i sin (\frac{13 π}{9}) 6 (1 + n^{4} - n^{5})^{\frac{2}{3}}

解答は

x = 3 3 - n^{5} + n^{4} + 1, x = - \frac{3 3 - n ^{5} + n ^{4} + 1}{2} + \frac{3 3 - n ^{5} + n ^{4} + 1 3}{2} i, x = - \frac{3 3 - n ^{5} + n ^{4} + 1}{2} - \frac{3 3 - n ^{5} + n ^{4} + 1 3}{2} i, x = cos (\frac{π}{9}) 6 (1 + n^{4} - n^{5})^{\frac{2}{3}} - i sin (\frac{π}{9}) 6 (1 + n^{4} - n^{5})^{\frac{2}{3}}, x = cos (\frac{5 π}{9}) 6 (1 + n^{4} - n^{5})^{\frac{2}{3}} + i sin (\frac{5 π}{9}) 6 (1 + n^{4} - n^{5})^{\frac{2}{3}}, x = cos (\frac{11 π}{9}) 6 (1 + n^{4} - n^{5})^{\frac{2}{3}} + i sin (\frac{11 π}{9}) 6 (1 + n^{4} - n^{5})^{\frac{2}{3}}, x = cos (\frac{π}{9}) 6 (1 + n^{4} - n^{5})^{\frac{2}{3}} + i sin (\frac{π}{9}) 6 (1 + n^{4} - n^{5})^{\frac{2}{3}}, x = cos (\frac{7 π}{9}) 6 (1 + n^{4} - n^{5})^{\frac{2}{3}} + i sin (\frac{7 π}{9}) 6 (1 + n^{4} - n^{5})^{\frac{2}{3}}, x = cos (\frac{13 π}{9}) 6 (1 + n^{4} - n^{5})^{\frac{2}{3}} + i sin (\frac{13 π}{9}) 6 (1 + n^{4} - n^{5})^{\frac{2}{3}}

グラフ

人気の例

z^{4} = (1 - i)^{4}

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

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

z^{4} + 1 = 0

x^{4} - 80 = 1

(x^2+5x-24)(x^2-3x+2)=(x^2+5x-24)(4x-10)

(x^{2} + 5 x - 24) (x^{2} - 3 x + 2) = (x^{2} + 5 x - 24) (4 x - 10)