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Beliebt Algebra >

(2x^2-7x)^2+2x^2-7x=20

Lösung

(2 x^{2} - 7 x)^{2} + 2 x^{2} - 7 x = 20

Lösung

x = 1, x = 4, x = - \frac{1}{2}, x = \frac{5}{2}

+1

Dezimale

x = 1, x = 4, x = - 0.5, x = 2.5

Schritte zur Lösung

(2 x^{2} - 7 x)^{2} + 2 x^{2} - 7 x = 20

Schreibe

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

um:

4 x^{4} - 28 x^{3} + 51 x^{2} - 7 x

4 x^{4} - 28 x^{3} + 51 x^{2} - 7 x = 20

Verschiebe

20

auf die linke Seite

4 x^{4} - 28 x^{3} + 51 x^{2} - 7 x - 20 = 0

Faktorisiere

4 x^{4} - 28 x^{3} + 51 x^{2} - 7 x - 20 : (x - 1) (x - 4) (2 x + 1) (2 x - 5)

(x - 1) (x - 4) (2 x + 1) (2 x - 5) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x - 1 = 0 or x - 4 = 0 or 2 x + 1 = 0 or 2 x - 5 = 0

Löse

x - 1 = 0 : x = 1

Löse

x - 4 = 0 : x = 4

Löse

2 x + 1 = 0 : x = - \frac{1}{2}

Löse

2 x - 5 = 0 : x = \frac{5}{2}

Die Lösungen sind

x = 1, x = 4, x = - \frac{1}{2}, x = \frac{5}{2}

Graph

Beliebte Beispiele

(x)^3+(3x)^2-x-3=0

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

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