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Beliebt Algebra >

(x^2-3x+3)(x^2-2x+3)=2x^2

Lösung

(x^{2} - 3 x + 3) (x^{2} - 2 x + 3) = 2 x^{2}

Lösung

x = 1, x = 3, x = \frac{1}{2} + i \frac{11}{2}, x = \frac{1}{2} - i \frac{11}{2}

Schritte zur Lösung

(x^{2} - 3 x + 3) (x^{2} - 2 x + 3) = 2 x^{2}

Schreibe

(x^{2} - 3 x + 3) (x^{2} - 2 x + 3)

um:

x^{4} - 5 x^{3} + 12 x^{2} - 15 x + 9

x^{4} - 5 x^{3} + 12 x^{2} - 15 x + 9 = 2 x^{2}

Verschiebe

2 x^{2}

auf die linke Seite

x^{4} - 5 x^{3} + 10 x^{2} - 15 x + 9 = 0

Faktorisiere

x^{4} - 5 x^{3} + 10 x^{2} - 15 x + 9 : (x - 1) (x - 3) (x^{2} - x + 3)

(x - 1) (x - 3) (x^{2} - x + 3) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x - 1 = 0 or x - 3 = 0 or x^{2} - x + 3 = 0

Löse

x - 1 = 0 : x = 1

Löse

x - 3 = 0 : x = 3

Löse

x^{2} - x + 3 = 0 : x = \frac{1}{2} + i \frac{11}{2}, x = \frac{1}{2} - i \frac{11}{2}

Die Lösungen sind

x = 1, x = 3, x = \frac{1}{2} + i \frac{11}{2}, x = \frac{1}{2} - i \frac{11}{2}

Graph

Beliebte Beispiele

y^{3} = y + 24

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

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