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Beliebt Algebra >

x(x+1)^2(x+2)=72

Lösung

x (x + 1)^{2} (x + 2) = 72

Lösung

x = 2, x = - 4, x = - 1 + 22 i, x = - 1 - 22 i

Schritte zur Lösung

x (x + 1)^{2} (x + 2) = 72

Schreibe

x (x + 1)^{2} (x + 2)

um:

x^{4} + 4 x^{3} + 5 x^{2} + 2 x

x^{4} + 4 x^{3} + 5 x^{2} + 2 x = 72

Verschiebe

72

auf die linke Seite

x^{4} + 4 x^{3} + 5 x^{2} + 2 x - 72 = 0

Faktorisiere

x^{4} + 4 x^{3} + 5 x^{2} + 2 x - 72 : (x - 2) (x + 4) (x^{2} + 2 x + 9)

(x - 2) (x + 4) (x^{2} + 2 x + 9) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x - 2 = 0 or x + 4 = 0 or x^{2} + 2 x + 9 = 0

Löse

x - 2 = 0 : x = 2

Löse

x + 4 = 0 : x = - 4

Löse

x^{2} + 2 x + 9 = 0 : x = - 1 + 22 i, x = - 1 - 22 i

Die Lösungen sind

x = 2, x = - 4, x = - 1 + 22 i, x = - 1 - 22 i

Graph

Beliebte Beispiele

4 x^{3} - 6 x^{2} = 0

(x+1)*(x+2)^2*(x+4)-2x^2=0

(x + 1) \cdot (x + 2)^{2} \cdot (x + 4) - 2 x^{2} = 0

z^4-11z^3+14z^2-11z+12=0

z^{4} - 11 z^{3} + 14 z^{2} - 11 z + 12 = 0

x^4+6x^3+6x^2+6x+5=0

x^{4} + 6 x^{3} + 6 x^{2} + 6 x + 5 = 0

solvefor a,a^5=b^4

so l v e f or a, a^{5} = b^{4}