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Beliebt Algebra >

x^{12}=3

Lösung

x^{12} = 3

Lösung

x = 63, x = - 63, x = 63 i, x = - 63 i, x = 0.94905 \dots + \frac{1.44224 \dots - 0.60046 \dots}{2} i, x = - 0.94905 \dots - \frac{1.44224 \dots - 0.60046 \dots}{2} i, x = - 0.54793 \dots + \frac{0.60046 \dots + 1.44224 \dots}{2} i, x = 0.54793 \dots - \frac{0.60046 \dots + 1.44224 \dots}{2} i, x = 0.54793 \dots + \frac{0.60046 \dots + 1.44224 \dots}{2} i, x = - 0.54793 \dots - \frac{0.60046 \dots + 1.44224 \dots}{2} i, x = - 0.94905 \dots + \frac{1.44224 \dots - 0.60046 \dots}{2} i, x = 0.94905 \dots - \frac{1.44224 \dots - 0.60046 \dots}{2} i

Schritte zur Lösung

x^{12} = 3

Schreibe die Gleichung um mit

u = x^{2}

und

u^{6} = x^{12}

u^{6} = 3

Löse

u^{6} = 3 : u = 33, u = - 33, u = \frac{3 ^{\frac{5}{6}}}{4.16016 \dots} + 1.04004 \dots i, u = - \frac{3 ^{\frac{5}{6}}}{4.16016 \dots} - 1.04004 \dots i, u = - \frac{3 ^{\frac{5}{6}}}{4.16016 \dots} + 1.04004 \dots i, u = \frac{3 ^{\frac{5}{6}}}{4.16016 \dots} - 1.04004 \dots i

u = 33, u = - 33, u = \frac{3 ^{\frac{5}{6}}}{4.16016 \dots} + 1.04004 \dots i, u = - \frac{3 ^{\frac{5}{6}}}{4.16016 \dots} - 1.04004 \dots i, u = - \frac{3 ^{\frac{5}{6}}}{4.16016 \dots} + 1.04004 \dots i, u = \frac{3 ^{\frac{5}{6}}}{4.16016 \dots} - 1.04004 \dots i

Setze

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

löse für

x

Löse

x^{2} = 33 : x = 63, x = - 63

Löse

x^{2} = - 33 : x = 63 i, x = - 63 i

Löse

x^{2} = \frac{3 ^{\frac{5}{6}}}{4.16016 \dots} + 1.04004 \dots i : x = 0.94905 \dots + \frac{1.44224 \dots - 0.60046 \dots}{2} i, x = - 0.94905 \dots - \frac{1.44224 \dots - 0.60046 \dots}{2} i

Löse

x^{2} = - \frac{3 ^{\frac{5}{6}}}{4.16016 \dots} - 1.04004 \dots i : x = - 0.54793 \dots + \frac{0.60046 \dots + 1.44224 \dots}{2} i, x = 0.54793 \dots - \frac{0.60046 \dots + 1.44224 \dots}{2} i

Löse

x^{2} = - \frac{3 ^{\frac{5}{6}}}{4.16016 \dots} + 1.04004 \dots i : x = 0.54793 \dots + \frac{0.60046 \dots + 1.44224 \dots}{2} i, x = - 0.54793 \dots - \frac{0.60046 \dots + 1.44224 \dots}{2} i

Löse

x^{2} = \frac{3 ^{\frac{5}{6}}}{4.16016 \dots} - 1.04004 \dots i : x = - 0.94905 \dots + \frac{1.44224 \dots - 0.60046 \dots}{2} i, x = 0.94905 \dots - \frac{1.44224 \dots - 0.60046 \dots}{2} i

Die Lösungen sind

x = 63, x = - 63, x = 63 i, x = - 63 i, x = 0.94905 \dots + \frac{1.44224 \dots - 0.60046 \dots}{2} i, x = - 0.94905 \dots - \frac{1.44224 \dots - 0.60046 \dots}{2} i, x = - 0.54793 \dots + \frac{0.60046 \dots + 1.44224 \dots}{2} i, x = 0.54793 \dots - \frac{0.60046 \dots + 1.44224 \dots}{2} i, x = 0.54793 \dots + \frac{0.60046 \dots + 1.44224 \dots}{2} i, x = - 0.54793 \dots - \frac{0.60046 \dots + 1.44224 \dots}{2} i, x = - 0.94905 \dots + \frac{1.44224 \dots - 0.60046 \dots}{2} i, x = 0.94905 \dots - \frac{1.44224 \dots - 0.60046 \dots}{2} i

Graph

Beliebte Beispiele

x^{12} = 7

x^{12} = 8

(2 + 3) \cdot x^{4} = 20

15 x^{4} - 20 x^{3} = 0

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