de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Algebra >

(5-2x)^3=-1

Lösung

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

Lösung

x = 3, x = \frac{9}{4} + i \frac{3}{4}, x = \frac{9}{4} - i \frac{3}{4}

Schritte zur Lösung

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

Schreibe

(5 - 2 x)^{3}

um:

125 - 150 x + 60 x^{2} - 8 x^{3}

125 - 150 x + 60 x^{2} - 8 x^{3} = - 1

Verschiebe

1

auf die linke Seite

- 8 x^{3} + 60 x^{2} - 150 x + 126 = 0

Faktorisiere

- 8 x^{3} + 60 x^{2} - 150 x + 126 : - 2 (x - 3) (4 x^{2} - 18 x + 21)

- 2 (x - 3) (4 x^{2} - 18 x + 21) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x - 3 = 0 or 4 x^{2} - 18 x + 21 = 0

Löse

x - 3 = 0 : x = 3

Löse

4 x^{2} - 18 x + 21 = 0 : x = \frac{9}{4} + i \frac{3}{4}, x = \frac{9}{4} - i \frac{3}{4}

Die Lösungen sind

x = 3, x = \frac{9}{4} + i \frac{3}{4}, x = \frac{9}{4} - i \frac{3}{4}

Graph

Beliebte Beispiele

x^4+x^3-8x^2-9x-9=0

x^{4} + x^{3} - 8 x^{2} - 9 x - 9 = 0

(x-3)(x-1)^2(x^2+4x+13)=0

(x - 3) (x - 1)^{2} (x^{2} + 4 x + 13) = 0

-2x^3+x^2+13x+6=0

- 2 x^{3} + x^{2} + 13 x + 6 = 0

x x^{2} = 4

(x^2-2)^2-2(x^2-2)-3=0

(x^{2} - 2)^{2} - 2 (x^{2} - 2) - 3 = 0