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Beliebt Algebra >

(r^2+5r)(r^2+5r+3)=4

Lösung

(r^{2} + 5 r) (r^{2} + 5 r + 3) = 4

Lösung

r = - 1, r = - 4, r = \frac{- 5 + 29}{2}, r = \frac{- 5 - 29}{2}

+1

Dezimale

r = - 1, r = - 4, r = 0.19258 \dots, r = - 5.19258 \dots

Schritte zur Lösung

(r^{2} + 5 r) (r^{2} + 5 r + 3) = 4

Schreibe

(r^{2} + 5 r) (r^{2} + 5 r + 3)

um:

r^{4} + 10 r^{3} + 28 r^{2} + 15 r

r^{4} + 10 r^{3} + 28 r^{2} + 15 r = 4

Verschiebe

4

auf die linke Seite

r^{4} + 10 r^{3} + 28 r^{2} + 15 r - 4 = 0

Faktorisiere

r^{4} + 10 r^{3} + 28 r^{2} + 15 r - 4 : (r + 1) (r + 4) (r^{2} + 5 r - 1)

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

r + 1 = 0 or r + 4 = 0 or r^{2} + 5 r - 1 = 0

Löse

r + 1 = 0 : r = - 1

Löse

r + 4 = 0 : r = - 4

Löse

r^{2} + 5 r - 1 = 0 : r = \frac{- 5 + 29}{2}, r = \frac{- 5 - 29}{2}

Die Lösungen sind

r = - 1, r = - 4, r = \frac{- 5 + 29}{2}, r = \frac{- 5 - 29}{2}

Graph

Beliebte Beispiele

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

-3x^4+25=-5+x^6

- 3 x^{4} + 25 = - 5 + x^{6}

x^{3} + 2 x^{2} - 15 x = 0

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

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

x^4+2x^3-26x^2-50x+25=0

x^{4} + 2 x^{3} - 26 x^{2} - 50 x + 25 = 0