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Beliebt Algebra >

(1-x)^7=(1-x)^5

Lösung

(1 - x)^{7} = (1 - x)^{5}

Lösung

x = 0, x = 1, x = 2

Schritte zur Lösung

(1 - x)^{7} = (1 - x)^{5}

Schreibe

(1 - x)^{7}

um:

1 - 7 x + 21 x^{2} - 35 x^{3} + 35 x^{4} - 21 x^{5} + 7 x^{6} - x^{7}

Schreibe

(1 - x)^{5}

um:

1 - 5 x + 10 x^{2} - 10 x^{3} + 5 x^{4} - x^{5}

1 - 7 x + 21 x^{2} - 35 x^{3} + 35 x^{4} - 21 x^{5} + 7 x^{6} - x^{7} = 1 - 5 x + 10 x^{2} - 10 x^{3} + 5 x^{4} - x^{5}

Verschiebe

1

auf die rechte Seite

- 7 x + 21 x^{2} - 35 x^{3} + 35 x^{4} - 21 x^{5} + 7 x^{6} - x^{7} = - x^{5} + 5 x^{4} - 10 x^{3} + 10 x^{2} - 5 x

Subtrahiere

- x^{5} + 5 x^{4} - 10 x^{3} + 10 x^{2} - 5 x

von beiden Seiten

- 7 x + 21 x^{2} - 35 x^{3} + 35 x^{4} - 21 x^{5} + 7 x^{6} - x^{7} - (- x^{5} + 5 x^{4} - 10 x^{3} + 10 x^{2} - 5 x) = - x^{5} + 5 x^{4} - 10 x^{3} + 10 x^{2} - 5 x - (- x^{5} + 5 x^{4} - 10 x^{3} + 10 x^{2} - 5 x)

Vereinfache

- x^{7} + 7 x^{6} - 20 x^{5} + 30 x^{4} - 25 x^{3} + 11 x^{2} - 2 x = 0

Faktorisiere

- x^{7} + 7 x^{6} - 20 x^{5} + 30 x^{4} - 25 x^{3} + 11 x^{2} - 2 x : - x (x - 1)^{5} (x - 2)

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x = 0 or x - 1 = 0 or x - 2 = 0

Löse

x - 1 = 0 : x = 1

Löse

x - 2 = 0 : x = 2

Die Lösungen sind

x = 0, x = 1, x = 2

Graph

Beliebte Beispiele

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

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

(x-2)^5=8(x-2)^3

(x - 2)^{5} = 8 (x - 2)^{3}

2x^3+3x^2-5x+74=3x^2+8x-6

2 x^{3} + 3 x^{2} - 5 x + 74 = 3 x^{2} + 8 x - 6

8 t^{2} - 4 t^{3} = - 60 t