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Beliebt Algebra >

x^8=3^{16}

Lösung

x^{8} = 3^{16}

Lösung

x = 9, x = - 9, x = 9 i, x = - 9 i, x = \frac{9}{2} + \frac{9}{2} i, x = - \frac{9}{2} - \frac{9}{2} i, x = \frac{9}{2} - \frac{9}{2} i, x = - \frac{9}{2} + \frac{9}{2} i

Schritte zur Lösung

x^{8} = 3^{16}

3^{16} = 43046721

x^{8} = 43046721

Schreibe die Gleichung um mit

u = x^{2}

und

u^{4} = x^{8}

u^{4} = 43046721

Löse

u^{4} = 43046721 : u = 81, u = - 81, u = 81 i, u = - 81 i

u = 81, u = - 81, u = 81 i, u = - 81 i

Setze

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

löse für

x

Löse

x^{2} = 81 : x = 9, x = - 9

Löse

x^{2} = - 81 : x = 9 i, x = - 9 i

Löse

x^{2} = 81 i : x = \frac{9}{2} + \frac{9}{2} i, x = - \frac{9}{2} - \frac{9}{2} i

Löse

x^{2} = - 81 i : x = \frac{9}{2} - \frac{9}{2} i, x = - \frac{9}{2} + \frac{9}{2} i

Die Lösungen sind

x = 9, x = - 9, x = 9 i, x = - 9 i, x = \frac{9}{2} + \frac{9}{2} i, x = - \frac{9}{2} - \frac{9}{2} i, x = \frac{9}{2} - \frac{9}{2} i, x = - \frac{9}{2} + \frac{9}{2} i

Graph

Beliebte Beispiele

-x^3-x^2+4x+4=0

- x^{3} - x^{2} + 4 x + 4 = 0

2h^4+17h^3+21h^2=h+7

2 h^{4} + 17 h^{3} + 21 h^{2} = h + 7

4 x^{4} - 4 x^{2} + 1 = 0

y^{2} (4 - y^{2}) = 0

5 x^{4} = 0