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Beliebt Algebra >

x(x+1)(x+2)(x+3)=461^2-1

Lösung

x (x + 1) (x + 2) (x + 3) = 46 1^{2} - 1

Lösung

x = 20, x = - 23, x = - \frac{3}{2} + i \frac{1839}{2}, x = - \frac{3}{2} - i \frac{1839}{2}

Schritte zur Lösung

x (x + 1) (x + 2) (x + 3) = 46 1^{2} - 1

Schreibe

x (x + 1) (x + 2) (x + 3)

um:

x^{4} + 6 x^{3} + 11 x^{2} + 6 x

Schreibe

46 1^{2} - 1

um:

212520

x^{4} + 6 x^{3} + 11 x^{2} + 6 x = 212520

Verschiebe

212520

auf die linke Seite

x^{4} + 6 x^{3} + 11 x^{2} + 6 x - 212520 = 0

Faktorisiere

x^{4} + 6 x^{3} + 11 x^{2} + 6 x - 212520 : (x - 20) (x + 23) (x^{2} + 3 x + 462)

(x - 20) (x + 23) (x^{2} + 3 x + 462) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x - 20 = 0 or x + 23 = 0 or x^{2} + 3 x + 462 = 0

Löse

x - 20 = 0 : x = 20

Löse

x + 23 = 0 : x = - 23

Löse

x^{2} + 3 x + 462 = 0 : x = - \frac{3}{2} + i \frac{1839}{2}, x = - \frac{3}{2} - i \frac{1839}{2}

Die Lösungen sind

x = 20, x = - 23, x = - \frac{3}{2} + i \frac{1839}{2}, x = - \frac{3}{2} - i \frac{1839}{2}

Graph

Beliebte Beispiele

473=(7pix^3)/(48)

473 = \frac{7 π x ^{3}}{48}

x^{4} - 7 = 0

6t(t^3-1)=7t^2(2t-1)-5t

6 t (t^{3} - 1) = 7 t^{2} (2 t - 1) - 5 t

solvefor z,(z-1)^4=-1

so l v e f or z, (z - 1)^{4} = - 1

18 = b (\frac{2 b}{3})^{2}