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Beliebt Algebra >

(x^2+4x)^2-17(x^2+4x)=60

Lösung

(x^{2} + 4 x)^{2} - 17 (x^{2} + 4 x) = 60

Lösung

x = - 1, x = - 3, x = 2 (6 - 1), x = - 2 (1 + 6)

+1

Dezimale

x = - 1, x = - 3, x = 2.89897 \dots, x = - 6.89897 \dots

Schritte zur Lösung

(x^{2} + 4 x)^{2} - 17 (x^{2} + 4 x) = 60

Schreibe

(x^{2} + 4 x)^{2} - 17 (x^{2} + 4 x)

um:

x^{4} + 8 x^{3} - x^{2} - 68 x

x^{4} + 8 x^{3} - x^{2} - 68 x = 60

Verschiebe

60

auf die linke Seite

x^{4} + 8 x^{3} - x^{2} - 68 x - 60 = 0

Faktorisiere

x^{4} + 8 x^{3} - x^{2} - 68 x - 60 : (x + 1) (x + 3) (x^{2} + 4 x - 20)

(x + 1) (x + 3) (x^{2} + 4 x - 20) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x + 1 = 0 or x + 3 = 0 or x^{2} + 4 x - 20 = 0

Löse

x + 1 = 0 : x = - 1

Löse

x + 3 = 0 : x = - 3

Löse

x^{2} + 4 x - 20 = 0 : x = 2 (6 - 1), x = - 2 (1 + 6)

Die Lösungen sind

x = - 1, x = - 3, x = 2 (6 - 1), x = - 2 (1 + 6)

Graph

Beliebte Beispiele

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

solvefor x,x^3-6x^2+6x+5=0

so l v e f or x, x^{3} - 6 x^{2} + 6 x + 5 = 0

(z^3+i-1)(1-2z+2z^2)=0

(z^{3} + i - 1) (1 - 2 z + 2 z^{2}) = 0

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

2x^3-14x^2+14x+30=0

2 x^{3} - 14 x^{2} + 14 x + 30 = 0