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Beliebt Algebra >

x^8+63x^4=64

Lösung

x^{8} + 63 x^{4} = 64

Lösung

x = 1, x = - 1, x = i, x = - i, x = 2 + 2 i, x = - 2 - 2 i, x = 2 - 2 i, x = - 2 + 2 i

Schritte zur Lösung

x^{8} + 63 x^{4} = 64

Verschiebe

64

auf die linke Seite

x^{8} + 63 x^{4} - 64 = 0

Schreibe die Gleichung um mit

u = x^{2}, u^{2} = x^{4}

und

u^{4} = x^{8}

u^{4} + 63 u^{2} - 64 = 0

Löse

u^{4} + 63 u^{2} - 64 = 0 : u = 1, u = - 1, u = 8 i, u = - 8 i

u = 1, u = - 1, u = 8 i, u = - 8 i

Setze

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

löse für

x

Löse

x^{2} = 1 : x = 1, x = - 1

Löse

x^{2} = - 1 : x = i, x = - i

Löse

x^{2} = 8 i : x = 2 + 2 i, x = - 2 - 2 i

Löse

x^{2} = - 8 i : x = 2 - 2 i, x = - 2 + 2 i

Die Lösungen sind

x = 1, x = - 1, x = i, x = - i, x = 2 + 2 i, x = - 2 - 2 i, x = 2 - 2 i, x = - 2 + 2 i

Graph

Beliebte Beispiele

z^6-2sqrt(3)z^4+4z^2=0

z^{6} - 23 z^{4} + 4 z^{2} = 0

x^3+2x^2+9x+18=0

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

z^{3} - 8 = 0

2x^4-47x^2-75=0

2 x^{4} - 47 x^{2} - 75 = 0

solvefor y,x=y^5

so l v e f or y, x = y^{5}