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Beliebt Algebra >

(x-7)^4=(x-7)^5

Lösung

(x - 7)^{4} = (x - 7)^{5}

Lösung

x = 7, x = 8

Schritte zur Lösung

(x - 7)^{4} = (x - 7)^{5}

Schreibe

(x - 7)^{4}

um:

x^{4} - 28 x^{3} + 294 x^{2} - 1372 x + 2401

Schreibe

(x - 7)^{5}

um:

x^{5} - 35 x^{4} + 490 x^{3} - 3430 x^{2} + 12005 x - 16807

x^{4} - 28 x^{3} + 294 x^{2} - 1372 x + 2401 = x^{5} - 35 x^{4} + 490 x^{3} - 3430 x^{2} + 12005 x - 16807

Tausche die Seiten

x^{5} - 35 x^{4} + 490 x^{3} - 3430 x^{2} + 12005 x - 16807 = x^{4} - 28 x^{3} + 294 x^{2} - 1372 x + 2401

Subtrahiere

x^{4} - 28 x^{3} + 294 x^{2} - 1372 x + 2401

von beiden Seiten

x^{5} - 35 x^{4} + 490 x^{3} - 3430 x^{2} + 12005 x - 16807 - (x^{4} - 28 x^{3} + 294 x^{2} - 1372 x + 2401) = x^{4} - 28 x^{3} + 294 x^{2} - 1372 x + 2401 - (x^{4} - 28 x^{3} + 294 x^{2} - 1372 x + 2401)

Vereinfache

x^{5} - 36 x^{4} + 518 x^{3} - 3724 x^{2} + 13377 x - 19208 = 0

Faktorisiere

x^{5} - 36 x^{4} + 518 x^{3} - 3724 x^{2} + 13377 x - 19208 : (x - 7)^{4} (x - 8)

(x - 7)^{4} (x - 8) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x - 7 = 0 or x - 8 = 0

Löse

x - 7 = 0 : x = 7

Löse

x - 8 = 0 : x = 8

Die Lösungen sind

x = 7, x = 8

Graph

Beliebte Beispiele

x^{3} = - 125

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

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

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

n^{3} - n - 990 = 0

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

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