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Beliebt Algebra >

x^6-25x^4-16x^2+400=0

Lösung

x^{6} - 25 x^{4} - 16 x^{2} + 400 = 0

Lösung

x = 5, x = - 5, x = 2 i, x = - 2 i, x = 2, x = - 2

Schritte zur Lösung

x^{6} - 25 x^{4} - 16 x^{2} + 400 = 0

Schreibe die Gleichung um mit

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

und

u^{3} = x^{6}

u^{3} - 25 u^{2} - 16 u + 400 = 0

Löse

u^{3} - 25 u^{2} - 16 u + 400 = 0 : u = 25, u = - 4, u = 4

u = 25, u = - 4, u = 4

Setze

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

löse für

x

Löse

x^{2} = 25 : x = 5, x = - 5

Löse

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

Löse

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

Die Lösungen sind

x = 5, x = - 5, x = 2 i, x = - 2 i, x = 2, x = - 2

Graph

Beliebte Beispiele

7 y^{3} + 17 y^{2} = 12 y

solvefor x,x^3+(y-1)^2=9

so l v e f or x, x^{3} + (y - 1)^{2} = 9

solvefor a,y=a^3+b^2

so l v e f or a, y = a^{3} + b^{2}

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

15 + x^{3} = 4 x^{2} + 15