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Beliebt Algebra >

x^{12}=7

Lösung

x^{12} = 7

Lösung

x = 67, x = - 67, x = 67 i, x = - 67 i, x = 1.01848 \dots + \frac{1.91293 \dots - 0.69154 \dots}{2} i, x = - 1.01848 \dots - \frac{1.91293 \dots - 0.69154 \dots}{2} i, x = - 0.58802 \dots + \frac{0.69154 \dots + 1.91293 \dots}{2} i, x = 0.58802 \dots - \frac{0.69154 \dots + 1.91293 \dots}{2} i, x = 0.58802 \dots + \frac{0.69154 \dots + 1.91293 \dots}{2} i, x = - 0.58802 \dots - \frac{0.69154 \dots + 1.91293 \dots}{2} i, x = - 1.01848 \dots + \frac{1.91293 \dots - 0.69154 \dots}{2} i, x = 1.01848 \dots - \frac{1.91293 \dots - 0.69154 \dots}{2} i

Schritte zur Lösung

x^{12} = 7

Schreibe die Gleichung um mit

u = x^{2}

und

u^{6} = x^{12}

u^{6} = 7

Löse

u^{6} = 7 : u = 37, u = - 37, u = 0.69154 \dots + 1.19778 \dots i, u = - 0.69154 \dots - 1.19778 \dots i, u = - 0.69154 \dots + 1.19778 \dots i, u = 0.69154 \dots - 1.19778 \dots i

u = 37, u = - 37, u = 0.69154 \dots + 1.19778 \dots i, u = - 0.69154 \dots - 1.19778 \dots i, u = - 0.69154 \dots + 1.19778 \dots i, u = 0.69154 \dots - 1.19778 \dots i

Setze

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

löse für

x

Löse

x^{2} = 37 : x = 67, x = - 67

Löse

x^{2} = - 37 : x = 67 i, x = - 67 i

Löse

x^{2} = 0.69154 \dots + 1.19778 \dots i : x = 1.01848 \dots + \frac{1.91293 \dots - 0.69154 \dots}{2} i, x = - 1.01848 \dots - \frac{1.91293 \dots - 0.69154 \dots}{2} i

Löse

x^{2} = - 0.69154 \dots - 1.19778 \dots i : x = - 0.58802 \dots + \frac{0.69154 \dots + 1.91293 \dots}{2} i, x = 0.58802 \dots - \frac{0.69154 \dots + 1.91293 \dots}{2} i

Löse

x^{2} = - 0.69154 \dots + 1.19778 \dots i : x = 0.58802 \dots + \frac{0.69154 \dots + 1.91293 \dots}{2} i, x = - 0.58802 \dots - \frac{0.69154 \dots + 1.91293 \dots}{2} i

Löse

x^{2} = 0.69154 \dots - 1.19778 \dots i : x = - 1.01848 \dots + \frac{1.91293 \dots - 0.69154 \dots}{2} i, x = 1.01848 \dots - \frac{1.91293 \dots - 0.69154 \dots}{2} i

Die Lösungen sind

x = 67, x = - 67, x = 67 i, x = - 67 i, x = 1.01848 \dots + \frac{1.91293 \dots - 0.69154 \dots}{2} i, x = - 1.01848 \dots - \frac{1.91293 \dots - 0.69154 \dots}{2} i, x = - 0.58802 \dots + \frac{0.69154 \dots + 1.91293 \dots}{2} i, x = 0.58802 \dots - \frac{0.69154 \dots + 1.91293 \dots}{2} i, x = 0.58802 \dots + \frac{0.69154 \dots + 1.91293 \dots}{2} i, x = - 0.58802 \dots - \frac{0.69154 \dots + 1.91293 \dots}{2} i, x = - 1.01848 \dots + \frac{1.91293 \dots - 0.69154 \dots}{2} i, x = 1.01848 \dots - \frac{1.91293 \dots - 0.69154 \dots}{2} i

Graph

Beliebte Beispiele

x^{12} = 8

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

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

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M=(x+5)(x-5)(x^2+25)+625

M = (x + 5) (x - 5) (x^{2} + 25) + 625