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Beliebt Algebra >

x^{12}=5000

Lösung

x^{12} = 5000

Lösung

x = 3252, x = - 3252, x = - 3252, x = - - 3252, x = - 1.01675 \dots + \frac{2.06759 \dots + 17.09975 \dots}{2} i, x = 1.01675 \dots - \frac{2.06759 \dots + 17.09975 \dots}{2} i, x = 1.76107 \dots + \frac{17.09975 \dots - 2.06759 \dots}{2} i, x = - 1.76107 \dots - \frac{17.09975 \dots - 2.06759 \dots}{2} i, x = - 1.76107 \dots + \frac{17.09975 \dots - 2.06759 \dots}{2} i, x = 1.76107 \dots - \frac{17.09975 \dots - 2.06759 \dots}{2} i, x = 1.01675 \dots + \frac{2.06759 \dots + 17.09975 \dots}{2} i, x = - 1.01675 \dots - \frac{2.06759 \dots + 17.09975 \dots}{2} i

Schritte zur Lösung

x^{12} = 5000

Schreibe die Gleichung um mit

u = x^{2}

und

u^{6} = x^{12}

u^{6} = 5000

Löse

u^{6} = 5000 : u = 3 5^{2} 2, u = - 3 5^{2} 2, u = - \frac{5 3 5 3}{7.16235 \dots} - 3.58117 \dots i, u = \frac{5 3 5 3}{7.16235 \dots} + 3.58117 \dots i, u = \frac{5 3 5 3}{7.16235 \dots} - 3.58117 \dots i, u = - \frac{5 3 5 3}{7.16235 \dots} + 3.58117 \dots i

u = 3 5^{2} 2, u = - 3 5^{2} 2, u = - \frac{5 3 5 3}{7.16235 \dots} - 3.58117 \dots i, u = \frac{5 3 5 3}{7.16235 \dots} + 3.58117 \dots i, u = \frac{5 3 5 3}{7.16235 \dots} - 3.58117 \dots i, u = - \frac{5 3 5 3}{7.16235 \dots} + 3.58117 \dots i

Setze

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

löse für

x

Löse

x^{2} = 3 5^{2} 2 : x = 3252, x = - 3252

Löse

x^{2} = - 3 5^{2} 2 : x = - 3252, x = - - 3252

Löse

x^{2} = - \frac{5 3 5 3}{7.16235 \dots} - 3.58117 \dots i : x = - 1.01675 \dots + \frac{2.06759 \dots + 17.09975 \dots}{2} i, x = 1.01675 \dots - \frac{2.06759 \dots + 17.09975 \dots}{2} i

Löse

x^{2} = \frac{5 3 5 3}{7.16235 \dots} + 3.58117 \dots i : x = 1.76107 \dots + \frac{17.09975 \dots - 2.06759 \dots}{2} i, x = - 1.76107 \dots - \frac{17.09975 \dots - 2.06759 \dots}{2} i

Löse

x^{2} = \frac{5 3 5 3}{7.16235 \dots} - 3.58117 \dots i : x = - 1.76107 \dots + \frac{17.09975 \dots - 2.06759 \dots}{2} i, x = 1.76107 \dots - \frac{17.09975 \dots - 2.06759 \dots}{2} i

Löse

x^{2} = - \frac{5 3 5 3}{7.16235 \dots} + 3.58117 \dots i : x = 1.01675 \dots + \frac{2.06759 \dots + 17.09975 \dots}{2} i, x = - 1.01675 \dots - \frac{2.06759 \dots + 17.09975 \dots}{2} i

Die Lösungen sind

x = 3252, x = - 3252, x = - 3252, x = - - 3252, x = - 1.01675 \dots + \frac{2.06759 \dots + 17.09975 \dots}{2} i, x = 1.01675 \dots - \frac{2.06759 \dots + 17.09975 \dots}{2} i, x = 1.76107 \dots + \frac{17.09975 \dots - 2.06759 \dots}{2} i, x = - 1.76107 \dots - \frac{17.09975 \dots - 2.06759 \dots}{2} i, x = - 1.76107 \dots + \frac{17.09975 \dots - 2.06759 \dots}{2} i, x = 1.76107 \dots - \frac{17.09975 \dots - 2.06759 \dots}{2} i, x = 1.01675 \dots + \frac{2.06759 \dots + 17.09975 \dots}{2} i, x = - 1.01675 \dots - \frac{2.06759 \dots + 17.09975 \dots}{2} i

Graph

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