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Beliebt Algebra >

-3=x^6-8

Lösung

- 3 = x^{6} - 8

Lösung

x = 35, x = - 35, x = \frac{- 3 5 + 2 5 ^{\frac{2}{3}}}{2} + \frac{3 5 3}{2 - 3 5 + 2 5 ^{\frac{2}{3}}} i, x = - \frac{- 3 5 + 2 5 ^{\frac{2}{3}}}{2} - \frac{3 5 3}{2 - 3 5 + 2 5 ^{\frac{2}{3}}} i, x = \frac{- 3 5 + 2 5 ^{\frac{2}{3}}}{2} - \frac{3 5 3}{2 - 3 5 + 2 5 ^{\frac{2}{3}}} i, x = - \frac{- 3 5 + 2 5 ^{\frac{2}{3}}}{2} + \frac{3 5 3}{2 - 3 5 + 2 5 ^{\frac{2}{3}}} i

Schritte zur Lösung

- 3 = x^{6} - 8

Tausche die Seiten

x^{6} - 8 = - 3

Verschiebe

8

auf die rechte Seite

x^{6} = 5

Schreibe die Gleichung um mit

u = x^{2}

und

u^{3} = x^{6}

u^{3} = 5

Löse

u^{3} = 5 : u = 35, u = 35 \frac{- 1 + 3 i}{2}, u = 35 \frac{- 1 - 3 i}{2}

u = 35, u = 35 \frac{- 1 + 3 i}{2}, u = 35 \frac{- 1 - 3 i}{2}

Setze

u = x^{2} w i e d er e in,

löse für

x

Löse

x^{2} = 35 : x = 35, x = - 35

Löse

x^{2} = 35 \frac{- 1 + 3 i}{2} : x = \frac{- 3 5 + 2 5 ^{\frac{2}{3}}}{2} + \frac{3 5 3}{2 - 3 5 + 2 5 ^{\frac{2}{3}}} i, x = - \frac{- 3 5 + 2 5 ^{\frac{2}{3}}}{2} - \frac{3 5 3}{2 - 3 5 + 2 5 ^{\frac{2}{3}}} i

Löse

x^{2} = 35 \frac{- 1 - 3 i}{2} : x = \frac{- 3 5 + 2 5 ^{\frac{2}{3}}}{2} - \frac{3 5 3}{2 - 3 5 + 2 5 ^{\frac{2}{3}}} i, x = - \frac{- 3 5 + 2 5 ^{\frac{2}{3}}}{2} + \frac{3 5 3}{2 - 3 5 + 2 5 ^{\frac{2}{3}}} i

Die Lösungen sind

x = 35, x = - 35, x = \frac{- 3 5 + 2 5 ^{\frac{2}{3}}}{2} + \frac{3 5 3}{2 - 3 5 + 2 5 ^{\frac{2}{3}}} i, x = - \frac{- 3 5 + 2 5 ^{\frac{2}{3}}}{2} - \frac{3 5 3}{2 - 3 5 + 2 5 ^{\frac{2}{3}}} i, x = \frac{- 3 5 + 2 5 ^{\frac{2}{3}}}{2} - \frac{3 5 3}{2 - 3 5 + 2 5 ^{\frac{2}{3}}} i, x = - \frac{- 3 5 + 2 5 ^{\frac{2}{3}}}{2} + \frac{3 5 3}{2 - 3 5 + 2 5 ^{\frac{2}{3}}} i

Graph

Beliebte Beispiele

x^2(x^2-4)=x^4(x^2-4)

x^{2} (x^{2} - 4) = x^{4} (x^{2} - 4)

x^{4} - 5 x^{3} + 4 = 0

x^3-x^2-x-25=470

x^{3} - x^{2} - x - 25 = 470

-x^3-x^2+8x+12=0

- x^{3} - x^{2} + 8 x + 12 = 0

2a^2(a^2+2)=27+7a^2

2 a^{2} (a^{2} + 2) = 27 + 7 a^{2}