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Beliebt Algebra >

(12x-1)(6x-1)(4x-1)(3x-1)=5

Lösung

(12 x - 1) (6 x - 1) (4 x - 1) (3 x - 1) = 5

Lösung

x = \frac{1}{2}, x = - \frac{1}{12}, x = \frac{5}{24} + i \frac{39}{24}, x = \frac{5}{24} - i \frac{39}{24}

Schritte zur Lösung

(12 x - 1) (6 x - 1) (4 x - 1) (3 x - 1) = 5

Schreibe

(12 x - 1) (6 x - 1) (4 x - 1) (3 x - 1)

um:

864 x^{4} - 720 x^{3} + 210 x^{2} - 25 x + 1

864 x^{4} - 720 x^{3} + 210 x^{2} - 25 x + 1 = 5

Verschiebe

5

auf die linke Seite

864 x^{4} - 720 x^{3} + 210 x^{2} - 25 x - 4 = 0

Faktorisiere

864 x^{4} - 720 x^{3} + 210 x^{2} - 25 x - 4 : (2 x - 1) (12 x + 1) (36 x^{2} - 15 x + 4)

(2 x - 1) (12 x + 1) (36 x^{2} - 15 x + 4) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

2 x - 1 = 0 or 12 x + 1 = 0 or 36 x^{2} - 15 x + 4 = 0

Löse

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

Löse

12 x + 1 = 0 : x = - \frac{1}{12}

Löse

36 x^{2} - 15 x + 4 = 0 : x = \frac{5}{24} + i \frac{39}{24}, x = \frac{5}{24} - i \frac{39}{24}

Die Lösungen sind

x = \frac{1}{2}, x = - \frac{1}{12}, x = \frac{5}{24} + i \frac{39}{24}, x = \frac{5}{24} - i \frac{39}{24}

Graph

Beliebte Beispiele

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

x^{3} + 4 x^{2} + x + 4 = 0

6 x^{4} - x^{2} - 1 = 0

0 = x^{3} - 13

z^{6} + 1 = 3 i