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Beliebt Algebra >

2(3x^4)=(2x^3)(2x^4)

Lösung

2 (3 x^{4}) = (2 x^{3}) (2 x^{4})

Lösung

x = 0, x = 3 \frac{3}{2}, x = - \frac{2 ^{\frac{2}{3}} 3 3}{4} + i \frac{3 2 3 6 ^{\frac{2}{3}}}{4}, x = - \frac{2 ^{\frac{2}{3}} 3 3}{4} - i \frac{3 2 3 6 ^{\frac{2}{3}}}{4}

Schritte zur Lösung

2 (3 x^{4}) = (2 x^{3}) (2 x^{4})

Verschiebe

(2 x^{3}) (2 x^{4})

auf die linke Seite

2 \cdot 3 x^{4} - 2 x^{3} \cdot 2 x^{4} = 0

Faktorisiere

2 \cdot 3 x^{4} - 2 x^{3} \cdot 2 x^{4} : - 2 x^{4} (32 x - 33) (2^{\frac{2}{3}} x^{2} + 36 x + 3^{\frac{2}{3}})

- 2 x^{4} (32 x - 33) (2^{\frac{2}{3}} x^{2} + 36 x + 3^{\frac{2}{3}}) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x = 0 or 32 x - 33 = 0 or 2^{\frac{2}{3}} x^{2} + 36 x + 3^{\frac{2}{3}} = 0

Löse

32 x - 33 = 0 : x = 3 \frac{3}{2}

Löse

2^{\frac{2}{3}} x^{2} + 36 x + 3^{\frac{2}{3}} = 0 : x = - \frac{2 ^{\frac{2}{3}} 3 3}{4} + i \frac{3 2 3 6 ^{\frac{2}{3}}}{4}, x = - \frac{2 ^{\frac{2}{3}} 3 3}{4} - i \frac{3 2 3 6 ^{\frac{2}{3}}}{4}

Die Lösungen sind

x = 0, x = 3 \frac{3}{2}, x = - \frac{2 ^{\frac{2}{3}} 3 3}{4} + i \frac{3 2 3 6 ^{\frac{2}{3}}}{4}, x = - \frac{2 ^{\frac{2}{3}} 3 3}{4} - i \frac{3 2 3 6 ^{\frac{2}{3}}}{4}

Graph

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