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Beliebt Algebra >

x^8=-256

Lösung

x^{8} = - 256

Lösung

x = 2 + 2 + 2 - 2 i, x = - 2 + 2 - 2 - 2 i, x = - 2 - 2 + 2 + 2 i, x = 2 - 2 - 2 + 2 i, x = 2 - 2 + 2 + 2 i, x = - 2 - 2 - 2 + 2 i, x = - 2 + 2 + 2 - 2 i, x = 2 + 2 - 2 - 2 i

Schritte zur Lösung

x^{8} = - 256

Schreibe die Gleichung um mit

u = x^{2}

und

u^{4} = x^{8}

u^{4} = - 256

Löse

u^{4} = - 256 : u = 22 + 22 i, u = - 22 - 22 i, u = - 22 + 22 i, u = 22 - 22 i

u = 22 + 22 i, u = - 22 - 22 i, u = - 22 + 22 i, u = 22 - 22 i

Setze

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

löse für

x

Löse

x^{2} = 22 + 22 i : x = 2 + 2 + 2 - 2 i, x = - 2 + 2 - 2 - 2 i

Löse

x^{2} = - 22 - 22 i : x = - 2 - 2 + 2 + 2 i, x = 2 - 2 - 2 + 2 i

Löse

x^{2} = - 22 + 22 i : x = 2 - 2 + 2 + 2 i, x = - 2 - 2 - 2 + 2 i

Löse

x^{2} = 22 - 22 i : x = - 2 + 2 + 2 - 2 i, x = 2 + 2 - 2 - 2 i

Die Lösungen sind

x = 2 + 2 + 2 - 2 i, x = - 2 + 2 - 2 - 2 i, x = - 2 - 2 + 2 + 2 i, x = 2 - 2 - 2 + 2 i, x = 2 - 2 + 2 + 2 i, x = - 2 - 2 - 2 + 2 i, x = - 2 + 2 + 2 - 2 i, x = 2 + 2 - 2 - 2 i

Graph

Beliebte Beispiele

wurzeln von x^4-4x^3+4x^2

roo t s x^{4} - 4 x^{3} + 4 x^{2}

4x^3+6x^2-72x-3=0

4 x^{3} + 6 x^{2} - 72 x - 3 = 0

wurzeln von x^3-2x-5

roo t s x^{3} - 2 x - 5

3(2-x)^3-2(2-x)^2-19(2-x)-6=0

3 (2 - x)^{3} - 2 (2 - x)^{2} - 19 (2 - x) - 6 = 0

x^3+2x^2+16x+32=0

x^{3} + 2 x^{2} + 16 x + 32 = 0