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Beliebt Algebra >

(9x-4)x^7=7x(9x-4)

Lösung

(9 x - 4) x^{7} = 7 x (9 x - 4)

Lösung

x = 0, x = \frac{4}{9}, x = - 67, x = 67, x = \frac{- 3 7 + 2 7 ^{\frac{2}{3}}}{2} + \frac{3 7 ^{\frac{2}{3}}}{2 - 3 7 + 2 7 ^{\frac{2}{3}}} i, x = - \frac{- 3 7 + 2 7 ^{\frac{2}{3}}}{2} - \frac{3 7 ^{\frac{2}{3}}}{2 - 3 7 + 2 7 ^{\frac{2}{3}}} i, x = \frac{- 3 7 + 2 7 ^{\frac{2}{3}}}{2} - \frac{3 7 ^{\frac{2}{3}}}{2 - 3 7 + 2 7 ^{\frac{2}{3}}} i, x = - \frac{- 3 7 + 2 7 ^{\frac{2}{3}}}{2} + \frac{3 7 ^{\frac{2}{3}}}{2 - 3 7 + 2 7 ^{\frac{2}{3}}} i

Schritte zur Lösung

(9 x - 4) x^{7} = 7 x (9 x - 4)

Verschiebe

7 x (9 x - 4)

auf die linke Seite

(9 x - 4) x^{7} - 7 x (9 x - 4) = 0

Faktorisiere

(9 x - 4) x^{7} - 7 x (9 x - 4) : x (9 x - 4) (x + 67) (x - 67) (x^{4} + 37 x^{2} + 7^{\frac{2}{3}})

x (9 x - 4) (x + 67) (x - 67) (x^{4} + 37 x^{2} + 7^{\frac{2}{3}}) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x = 0 or 9 x - 4 = 0 or x + 67 = 0 or x - 67 = 0 or x^{4} + 37 x^{2} + 7^{\frac{2}{3}} = 0

Löse

9 x - 4 = 0 : x = \frac{4}{9}

Löse

x + 67 = 0 : x = - 67

Löse

x - 67 = 0 : x = 67

Löse

x^{4} + 37 x^{2} + 7^{\frac{2}{3}} = 0 : x = \frac{- 3 7 + 2 7 ^{\frac{2}{3}}}{2} + \frac{3 7 ^{\frac{2}{3}}}{2 - 3 7 + 2 7 ^{\frac{2}{3}}} i, x = - \frac{- 3 7 + 2 7 ^{\frac{2}{3}}}{2} - \frac{3 7 ^{\frac{2}{3}}}{2 - 3 7 + 2 7 ^{\frac{2}{3}}} i, x = \frac{- 3 7 + 2 7 ^{\frac{2}{3}}}{2} - \frac{3 7 ^{\frac{2}{3}}}{2 - 3 7 + 2 7 ^{\frac{2}{3}}} i, x = - \frac{- 3 7 + 2 7 ^{\frac{2}{3}}}{2} + \frac{3 7 ^{\frac{2}{3}}}{2 - 3 7 + 2 7 ^{\frac{2}{3}}} i

Die Lösungen sind

x = 0, x = \frac{4}{9}, x = - 67, x = 67, x = \frac{- 3 7 + 2 7 ^{\frac{2}{3}}}{2} + \frac{3 7 ^{\frac{2}{3}}}{2 - 3 7 + 2 7 ^{\frac{2}{3}}} i, x = - \frac{- 3 7 + 2 7 ^{\frac{2}{3}}}{2} - \frac{3 7 ^{\frac{2}{3}}}{2 - 3 7 + 2 7 ^{\frac{2}{3}}} i, x = \frac{- 3 7 + 2 7 ^{\frac{2}{3}}}{2} - \frac{3 7 ^{\frac{2}{3}}}{2 - 3 7 + 2 7 ^{\frac{2}{3}}} i, x = - \frac{- 3 7 + 2 7 ^{\frac{2}{3}}}{2} + \frac{3 7 ^{\frac{2}{3}}}{2 - 3 7 + 2 7 ^{\frac{2}{3}}} i

Graph

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