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Beliebt Algebra >

(1-3x)^4-5(1-3x)^2+4=0

Lösung

(1 - 3 x)^{4} - 5 (1 - 3 x)^{2} + 4 = 0

Lösung

x = 0, x = 1, x = - \frac{1}{3}, x = \frac{2}{3}

+1

Dezimale

x = 0, x = 1, x = - 0.33333 \dots, x = 0.66666 \dots

Schritte zur Lösung

(1 - 3 x)^{4} - 5 (1 - 3 x)^{2} + 4 = 0

Schreibe

(1 - 3 x)^{4} - 5 (1 - 3 x)^{2} + 4

um:

81 x^{4} - 108 x^{3} + 9 x^{2} + 18 x

81 x^{4} - 108 x^{3} + 9 x^{2} + 18 x = 0

Faktorisiere

81 x^{4} - 108 x^{3} + 9 x^{2} + 18 x : 9 x (x - 1) (3 x + 1) (3 x - 2)

9 x (x - 1) (3 x + 1) (3 x - 2) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x = 0 or x - 1 = 0 or 3 x + 1 = 0 or 3 x - 2 = 0

Löse

x - 1 = 0 : x = 1

Löse

3 x + 1 = 0 : x = - \frac{1}{3}

Löse

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

Die Lösungen sind

x = 0, x = 1, x = - \frac{1}{3}, x = \frac{2}{3}

Graph

Beliebte Beispiele

0 = 4 x^{3} + 16 x - 20

x^3-6x^2+3x+1=0

x^{3} - 6 x^{2} + 3 x + 1 = 0

y^3+4y^2-36y=144

y^{3} + 4 y^{2} - 36 y = 144

x^3-8x^2+20x-16=0

x^{3} - 8 x^{2} + 20 x - 16 = 0

2870=1000*(1+x)^5

2870 = 1000 \cdot (1 + x)^{5}