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Beliebt Algebra >

x^9+3x^6+3x^3-16x+9=0

Lösung

x^{9} + 3 x^{6} + 3 x^{3} - 16 x + 9 = 0

Lösung

x = 1, x \approx 0.61803 \dots, x \approx - 1.61803 \dots

Schritte zur Lösung

x^{9} + 3 x^{6} + 3 x^{3} - 16 x + 9 = 0

Faktorisiere

x^{9} + 3 x^{6} + 3 x^{3} - 16 x + 9 : (x - 1) (x^{8} + x^{7} + x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 7 x^{2} + 7 x - 9)

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

x - 1 = 0 : x = 1

Löse

x^{8} + x^{7} + x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 7 x^{2} + 7 x - 9 = 0 : x \approx 0.61803 \dots, x \approx - 1.61803 \dots

Die Lösungen sind

x = 1, x \approx 0.61803 \dots, x \approx - 1.61803 \dots

Graph

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