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Beliebt Algebra >

x^8=2

Lösung

x^{8} = 2

Lösung

x = 42, x = - 42, x = 42 i, x = - 42 i, x = \frac{1}{8 2 ^{3}} + \frac{1}{8 2 ^{3}} i, x = - \frac{1}{8 2 ^{3}} - \frac{1}{8 2 ^{3}} i, x = \frac{1}{8 2 ^{3}} - \frac{1}{8 2 ^{3}} i, x = - \frac{1}{8 2 ^{3}} + \frac{1}{8 2 ^{3}} i

Schritte zur Lösung

x^{8} = 2

Schreibe die Gleichung um mit

u = x^{2}

und

u^{4} = x^{8}

u^{4} = 2

Löse

u^{4} = 2 : u = 2, u = - 2, u = 2 i, u = - 2 i

u = 2, u = - 2, u = 2 i, u = - 2 i

Setze

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

löse für

x

Löse

x^{2} = 2 : x = 42, x = - 42

Löse

x^{2} = - 2 : x = 42 i, x = - 42 i

Löse

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

Löse

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

Die Lösungen sind

x = 42, x = - 42, x = 42 i, x = - 42 i, x = \frac{1}{8 2 ^{3}} + \frac{1}{8 2 ^{3}} i, x = - \frac{1}{8 2 ^{3}} - \frac{1}{8 2 ^{3}} i, x = \frac{1}{8 2 ^{3}} - \frac{1}{8 2 ^{3}} i, x = - \frac{1}{8 2 ^{3}} + \frac{1}{8 2 ^{3}} i

Graph

Beliebte Beispiele

x^3+2bx^2-9x-18b=0

x^{3} + 2 b x^{2} - 9 x - 18 b = 0

x^{3} = - 5

(x^{2})^{3} = x

16 x^{4} - 1 = 0

x^{4} - 64 = 0