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Beliebt Algebra >

x^6=30

Lösung

x^{6} = 30

Lösung

x = 330, x = - 330, x = 0.88136 \dots + \frac{3 ^{\frac{5}{6}} 3 5}{2 ^{\frac{2}{3}} \cdot 1.76273 \dots} i, x = - 0.88136 \dots - \frac{3 ^{\frac{5}{6}} 3 5}{2 ^{\frac{2}{3}} \cdot 1.76273 \dots} i, x = 0.88136 \dots - \frac{3 ^{\frac{5}{6}} 3 5}{2 ^{\frac{2}{3}} \cdot 1.76273 \dots} i, x = - 0.88136 \dots + \frac{3 ^{\frac{5}{6}} 3 5}{2 ^{\frac{2}{3}} \cdot 1.76273 \dots} i

Schritte zur Lösung

x^{6} = 30

Schreibe die Gleichung um mit

u = x^{2}

und

u^{3} = x^{6}

u^{3} = 30

Löse

u^{3} = 30 : u = 330, u = 330 \frac{- 1 + 3 i}{2}, u = 330 \frac{- 1 - 3 i}{2}

u = 330, u = 330 \frac{- 1 + 3 i}{2}, u = 330 \frac{- 1 - 3 i}{2}

Setze

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

löse für

x

Löse

x^{2} = 330 : x = 330, x = - 330

Löse

x^{2} = 330 \frac{- 1 + 3 i}{2} : x = 0.88136 \dots + \frac{3 ^{\frac{5}{6}} 3 5}{2 ^{\frac{2}{3}} \cdot 1.76273 \dots} i, x = - 0.88136 \dots - \frac{3 ^{\frac{5}{6}} 3 5}{2 ^{\frac{2}{3}} \cdot 1.76273 \dots} i

Löse

x^{2} = 330 \frac{- 1 - 3 i}{2} : x = 0.88136 \dots - \frac{3 ^{\frac{5}{6}} 3 5}{2 ^{\frac{2}{3}} \cdot 1.76273 \dots} i, x = - 0.88136 \dots + \frac{3 ^{\frac{5}{6}} 3 5}{2 ^{\frac{2}{3}} \cdot 1.76273 \dots} i

Die Lösungen sind

x = 330, x = - 330, x = 0.88136 \dots + \frac{3 ^{\frac{5}{6}} 3 5}{2 ^{\frac{2}{3}} \cdot 1.76273 \dots} i, x = - 0.88136 \dots - \frac{3 ^{\frac{5}{6}} 3 5}{2 ^{\frac{2}{3}} \cdot 1.76273 \dots} i, x = 0.88136 \dots - \frac{3 ^{\frac{5}{6}} 3 5}{2 ^{\frac{2}{3}} \cdot 1.76273 \dots} i, x = - 0.88136 \dots + \frac{3 ^{\frac{5}{6}} 3 5}{2 ^{\frac{2}{3}} \cdot 1.76273 \dots} i

Graph

Beliebte Beispiele

2 x^{4} = 8

a=(a-3)(a+3)(a^2-3a+9)(a^2+3a+9)

a = (a - 3) (a + 3) (a^{2} - 3 a + 9) (a^{2} + 3 a + 9)

x^{6} = - 64

x^{5} - i = 0

k^{4} - 2 k^{2} - 8 = 0