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Beliebt Algebra >

(2x^2-1)(x+2)(x^2-2x)(x^3+5)=0

Lösung

(2 x^{2} - 1) (x + 2) (x^{2} - 2 x) (x^{3} + 5) = 0

Lösung

x = 0, x = - 2, x = 2, x = - \frac{1}{2}, x = \frac{1}{2}, x = - 35, x = \frac{3 5}{2} + i \frac{3 5 ^{\frac{2}{3}}}{2}, x = \frac{3 5}{2} - i \frac{3 5 ^{\frac{2}{3}}}{2}

Schritte zur Lösung

(2 x^{2} - 1) (x + 2) (x^{2} - 2 x) (x^{3} + 5) = 0

Faktorisiere

(2 x^{2} - 1) (x + 2) (x^{2} - 2 x) (x^{3} + 5) : x (x + 2) (x - 2) (2 x + 1) (2 x - 1) (x + 35) (x^{2} - 35 x + 5^{\frac{2}{3}})

x (x + 2) (x - 2) (2 x + 1) (2 x - 1) (x + 35) (x^{2} - 35 x + 5^{\frac{2}{3}}) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x = 0 or x + 2 = 0 or x - 2 = 0 or 2 x + 1 = 0 or 2 x - 1 = 0 or x + 35 = 0 or x^{2} - 35 x + 5^{\frac{2}{3}} = 0

Löse

x + 2 = 0 : x = - 2

Löse

x - 2 = 0 : x = 2

Löse

2 x + 1 = 0 : x = - \frac{1}{2}

Löse

2 x - 1 = 0 : x = \frac{1}{2}

Löse

x + 35 = 0 : x = - 35

Löse

x^{2} - 35 x + 5^{\frac{2}{3}} = 0 : x = \frac{3 5}{2} + i \frac{3 5 ^{\frac{2}{3}}}{2}, x = \frac{3 5}{2} - i \frac{3 5 ^{\frac{2}{3}}}{2}

Die Lösungen sind

x = 0, x = - 2, x = 2, x = - \frac{1}{2}, x = \frac{1}{2}, x = - 35, x = \frac{3 5}{2} + i \frac{3 5 ^{\frac{2}{3}}}{2}, x = \frac{3 5}{2} - i \frac{3 5 ^{\frac{2}{3}}}{2}

Graph

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