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Beliebt Algebra >

(3x^2)5=3(2x^5)

Lösung

(3 x^{2}) 5 = 3 (2 x^{5})

Lösung

x = 0, x = 3 \frac{5}{2}, x = - \frac{2 ^{\frac{2}{3}} 3 5}{4} + i \frac{3 2 3 1 0 ^{\frac{2}{3}}}{4}, x = - \frac{2 ^{\frac{2}{3}} 3 5}{4} - i \frac{3 2 3 1 0 ^{\frac{2}{3}}}{4}

Schritte zur Lösung

(3 x^{2}) \cdot 5 = 3 (2 x^{5})

Verschiebe

3 (2 x^{5})

auf die linke Seite

3 x^{2} \cdot 5 - 3 \cdot 2 x^{5} = 0

Faktorisiere

3 x^{2} \cdot 5 - 3 \cdot 2 x^{5} : - 3 x^{2} (32 x - 35) (2^{\frac{2}{3}} x^{2} + 310 x + 5^{\frac{2}{3}})

- 3 x^{2} (32 x - 35) (2^{\frac{2}{3}} x^{2} + 310 x + 5^{\frac{2}{3}}) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x = 0 or 32 x - 35 = 0 or 2^{\frac{2}{3}} x^{2} + 310 x + 5^{\frac{2}{3}} = 0

Löse

32 x - 35 = 0 : x = 3 \frac{5}{2}

Löse

2^{\frac{2}{3}} x^{2} + 310 x + 5^{\frac{2}{3}} = 0 : x = - \frac{2 ^{\frac{2}{3}} 3 5}{4} + i \frac{3 2 3 1 0 ^{\frac{2}{3}}}{4}, x = - \frac{2 ^{\frac{2}{3}} 3 5}{4} - i \frac{3 2 3 1 0 ^{\frac{2}{3}}}{4}

Die Lösungen sind

x = 0, x = 3 \frac{5}{2}, x = - \frac{2 ^{\frac{2}{3}} 3 5}{4} + i \frac{3 2 3 1 0 ^{\frac{2}{3}}}{4}, x = - \frac{2 ^{\frac{2}{3}} 3 5}{4} - i \frac{3 2 3 1 0 ^{\frac{2}{3}}}{4}

Graph

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