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Beliebt Algebra >

2^3=x^{12}

Lösung

2^{3} = x^{12}

Lösung

x = 2, x = - 2, x = 2 i, x = - 2 i, x = \frac{\frac{3}{2}}{4 2} + \frac{1}{4 2 ^{3}} i, x = - \frac{\frac{3}{2}}{4 2} - \frac{1}{4 2 ^{3}} i, x = - \frac{\frac{3}{2}}{4 2 3} + \frac{3}{4 2 ^{3}} i, x = \frac{\frac{3}{2}}{4 2 3} - \frac{3}{4 2 ^{3}} i, x = \frac{\frac{3}{2}}{4 2 3} + \frac{3}{4 2 ^{3}} i, x = - \frac{\frac{3}{2}}{4 2 3} - \frac{3}{4 2 ^{3}} i, x = - \frac{\frac{3}{2}}{4 2} + \frac{1}{4 2 ^{3}} i, x = \frac{\frac{3}{2}}{4 2} - \frac{1}{4 2 ^{3}} i

Schritte zur Lösung

2^{3} = x^{12}

Tausche die Seiten

x^{12} = 2^{3}

2^{3} = 8

x^{12} = 8

Schreibe die Gleichung um mit

u = x^{2}

und

u^{6} = x^{12}

u^{6} = 8

Löse

u^{6} = 8 : u = 2, u = - 2, u = \frac{1}{2} + \frac{3}{2} i, u = - \frac{1}{2} - \frac{3}{2} i, u = - \frac{1}{2} + \frac{3}{2} i, u = \frac{3}{2 \frac{3}{2}} - \frac{3}{2} i

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

Setze

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

löse für

x

Löse

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

Löse

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

Löse

x^{2} = \frac{1}{2} + \frac{3}{2} i : x = \frac{\frac{3}{2}}{4 2} + \frac{1}{4 2 ^{3}} i, x = - \frac{\frac{3}{2}}{4 2} - \frac{1}{4 2 ^{3}} i

Löse

x^{2} = - \frac{1}{2} - \frac{3}{2} i : x = - \frac{\frac{3}{2}}{4 2 3} + \frac{3}{4 2 ^{3}} i, x = \frac{\frac{3}{2}}{4 2 3} - \frac{3}{4 2 ^{3}} i

Löse

x^{2} = - \frac{1}{2} + \frac{3}{2} i : x = \frac{\frac{3}{2}}{4 2 3} + \frac{3}{4 2 ^{3}} i, x = - \frac{\frac{3}{2}}{4 2 3} - \frac{3}{4 2 ^{3}} i

Löse

x^{2} = \frac{3}{2 \frac{3}{2}} - \frac{3}{2} i : x = - \frac{\frac{3}{2}}{4 2} + \frac{1}{4 2 ^{3}} i, x = \frac{\frac{3}{2}}{4 2} - \frac{1}{4 2 ^{3}} i

Die Lösungen sind

x = 2, x = - 2, x = 2 i, x = - 2 i, x = \frac{\frac{3}{2}}{4 2} + \frac{1}{4 2 ^{3}} i, x = - \frac{\frac{3}{2}}{4 2} - \frac{1}{4 2 ^{3}} i, x = - \frac{\frac{3}{2}}{4 2 3} + \frac{3}{4 2 ^{3}} i, x = \frac{\frac{3}{2}}{4 2 3} - \frac{3}{4 2 ^{3}} i, x = \frac{\frac{3}{2}}{4 2 3} + \frac{3}{4 2 ^{3}} i, x = - \frac{\frac{3}{2}}{4 2 3} - \frac{3}{4 2 ^{3}} i, x = - \frac{\frac{3}{2}}{4 2} + \frac{1}{4 2 ^{3}} i, x = \frac{\frac{3}{2}}{4 2} - \frac{1}{4 2 ^{3}} i

Graph

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