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Beliebt Algebra >

x^4-8x^9-9=0

Lösung

x^{4} - 8 x^{9} - 9 = 0

Lösung

x = - 1

Schritte zur Lösung

x^{4} - 8 x^{9} - 9 = 0

Schreibe in der Standard Form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

- 8 x^{9} + x^{4} - 9 = 0

Faktorisiere

- 8 x^{9} + x^{4} - 9 : - (x + 1) (8 x^{8} - 8 x^{7} + 8 x^{6} - 8 x^{5} + 8 x^{4} - 9 x^{3} + 9 x^{2} - 9 x + 9)

- (x + 1) (8 x^{8} - 8 x^{7} + 8 x^{6} - 8 x^{5} + 8 x^{4} - 9 x^{3} + 9 x^{2} - 9 x + 9) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x + 1 = 0 or 8 x^{8} - 8 x^{7} + 8 x^{6} - 8 x^{5} + 8 x^{4} - 9 x^{3} + 9 x^{2} - 9 x + 9 = 0

Löse

x + 1 = 0 : x = - 1

Löse

8 x^{8} - 8 x^{7} + 8 x^{6} - 8 x^{5} + 8 x^{4} - 9 x^{3} + 9 x^{2} - 9 x + 9 = 0 :

Keine Lösung für

x \in R

Deshalb ist die Lösung

x = - 1

Graph

Beliebte Beispiele

(m^2+1)^3(m^2+m+1)^2=0

(m^{2} + 1)^{3} (m^{2} + m + 1)^{2} = 0

x^{3} + x = - 1

10 x^{3} + 3 x - 4 = 0

2x^3x^3x^2=6144

2 x^{3} x^{3} x^{2} = 6144

(2x+1)^2-(x^2+2)(x^2-2)=4,x+1/4-3=4

(2 x + 1)^{2} - (x^{2} + 2) (x^{2} - 2) = 4, x + \frac{1}{4} - 3 = 4