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Beliebt Algebra >

(x^2-5x)^2-7(x^2-5x)+6=0

Lösung

(x^{2} - 5 x)^{2} - 7 (x^{2} - 5 x) + 6 = 0

Lösung

x = - 1, x = 6, x = \frac{5 + 29}{2}, x = \frac{5 - 29}{2}

+1

Dezimale

x = - 1, x = 6, x = 5.19258 \dots, x = - 0.19258 \dots

Schritte zur Lösung

(x^{2} - 5 x)^{2} - 7 (x^{2} - 5 x) + 6 = 0

Schreibe

(x^{2} - 5 x)^{2} - 7 (x^{2} - 5 x) + 6

um:

x^{4} - 10 x^{3} + 18 x^{2} + 35 x + 6

x^{4} - 10 x^{3} + 18 x^{2} + 35 x + 6 = 0

Faktorisiere

x^{4} - 10 x^{3} + 18 x^{2} + 35 x + 6 : (x + 1) (x - 6) (x^{2} - 5 x - 1)

(x + 1) (x - 6) (x^{2} - 5 x - 1) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x + 1 = 0 or x - 6 = 0 or x^{2} - 5 x - 1 = 0

Löse

x + 1 = 0 : x = - 1

Löse

x - 6 = 0 : x = 6

Löse

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

Die Lösungen sind

x = - 1, x = 6, x = \frac{5 + 29}{2}, x = \frac{5 - 29}{2}

Graph

Beliebte Beispiele

n^{3} - n - 990 = 0

x^3-3x^2-25x+75=0

x^{3} - 3 x^{2} - 25 x + 75 = 0

2 x = (35 x^{6}) - 178

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

x^{3} + 5 x - 774 = 0