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Beliebt Algebra >

(7^2)^4=n^8

Lösung

(7^{2})^{4} = n^{8}

Lösung

n = 49, n = - 49, n = 7 i, n = - 7 i, n = \frac{7}{2} + \frac{7}{2} i, n = - \frac{7}{2} - \frac{7}{2} i, n = \frac{7}{2} - \frac{7}{2} i, n = - \frac{7}{2} + \frac{7}{2} i

Schritte zur Lösung

(7^{2})^{4} = n^{8}

Tausche die Seiten

n^{8} = (7^{2})^{4}

Vereinfache

(7^{2})^{4} : 5764801

Schreibe die Gleichung um mit

u = n^{2}

und

u^{4} = n^{8}

u^{4} = 5764801

Löse

u^{4} = 5764801 : u = 49, u = - 49, u = 49 i, u = - 49 i

u = 49, u = - 49, u = 49 i, u = - 49 i

Setze

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

löse für

n

Löse

n^{2} = 49 : n = 49, n = - 49

Löse

n^{2} = - 49 : n = 7 i, n = - 7 i

Löse

n^{2} = 49 i : n = \frac{7}{2} + \frac{7}{2} i, n = - \frac{7}{2} - \frac{7}{2} i

Löse

n^{2} = - 49 i : n = \frac{7}{2} - \frac{7}{2} i, n = - \frac{7}{2} + \frac{7}{2} i

Die Lösungen sind

n = 49, n = - 49, n = 7 i, n = - 7 i, n = \frac{7}{2} + \frac{7}{2} i, n = - \frac{7}{2} - \frac{7}{2} i, n = \frac{7}{2} - \frac{7}{2} i, n = - \frac{7}{2} + \frac{7}{2} i

Graph

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