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Beliebt Algebra >

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

Lösung

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

Lösung

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}}

Schritte zur Lösung

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

Verschiebe

n^{5}

auf die rechte Seite

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

Verschiebe

n^{4}

auf die rechte Seite

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

Verschiebe

1

auf die rechte Seite

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

Schreibe die Gleichung um mit

u = x^{3}

und

u^{3} = x^{9}

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

Löse

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}

Setze

u = x^{3} w i e d er e in,

löse für

x

Löse

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

Löse

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}}

Löse

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}}

Die Lösungen sind

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}}

Graph

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