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Beliebt Algebra >

x^8-17x^4+16=0

Lösung

x^{8} - 17 x^{4} + 16 = 0

Lösung

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

Schritte zur Lösung

x^{8} - 17 x^{4} + 16 = 0

Schreibe die Gleichung um mit

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

und

u^{4} = x^{8}

u^{4} - 17 u^{2} + 16 = 0

Löse

u^{4} - 17 u^{2} + 16 = 0 : u = 4, u = - 4, u = 1, u = - 1

u = 4, u = - 4, u = 1, u = - 1

Setze

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

löse für

x

Löse

x^{2} = 4 : x = 2, x = - 2

Löse

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

Löse

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

Löse

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

Die Lösungen sind

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

Graph

Beliebte Beispiele

x^{3} + 8 i = 0

solvefor x,x^3-x^2+x-2=4

so l v e f or x, x^{3} - x^{2} + x - 2 = 4

(x^2+x)^2-18(x^2+x)+72=0

(x^{2} + x)^{2} - 18 (x^{2} + x) + 72 = 0

(w-3)(w^2+3w+9)=2

(w - 3) (w^{2} + 3 w + 9) = 2

x^6-5x^4+6x^2-1=0

x^{6} - 5 x^{4} + 6 x^{2} - 1 = 0