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Beliebt Algebra >

2x^3-3x=sqrt(1-x^2)(1-6x)

Lösung

2 x^{3} - 3 x = 1 - x^{2} (1 - 6 x)

Lösung

x \approx 0.32765 \dots, x \approx - 0.98884 \dots, x \approx 0.97536 \dots

Schritte zur Lösung

2 x^{3} - 3 x = 1 - x^{2} (1 - 6 x)

Schreibe

1 - x^{2} (1 - 6 x)

um:

1 - x^{2} - 6 1 - x^{2} x

2 x^{3} - 3 x = 1 - x^{2} - 6 1 - x^{2} x

Faktorisiere

2 x^{3} - 3 x : x (2 x + 3) (2 x - 3)

Faktorisiere

1 - x^{2} - 6 1 - x^{2} x : - (6 x - 1) - (x + 1) (x - 1)

x (2 x + 3) (2 x - 3) = - (6 x - 1) - (x + 1) (x - 1)

Quadriere beide Seiten:

4 x^{6} - 12 x^{4} + 9 x^{2} = - 36 x^{4} + 12 x^{3} + 35 x^{2} - 12 x + 1

4 x^{6} - 12 x^{4} + 9 x^{2} = - 36 x^{4} + 12 x^{3} + 35 x^{2} - 12 x + 1

Löse

4 x^{6} - 12 x^{4} + 9 x^{2} = - 36 x^{4} + 12 x^{3} + 35 x^{2} - 12 x + 1 : x \approx 0.11118 \dots, x \approx 0.32765 \dots, x \approx - 0.98884 \dots, x \approx 0.97536 \dots

x \approx 0.11118 \dots, x \approx 0.32765 \dots, x \approx - 0.98884 \dots, x \approx 0.97536 \dots

Überprüfe die Lösungen:

x \approx 0.11118 \dots

Falsch

, x \approx 0.32765 \dots

Wahr

, x \approx - 0.98884 \dots

Wahr

, x \approx 0.97536 \dots

Wahr

Die Lösungen sind

x \approx 0.32765 \dots, x \approx - 0.98884 \dots, x \approx 0.97536 \dots

Graph

Beliebte Beispiele

sqrt(2a)=sqrt(8)

2 a = 8

x - 2 = x + 2

- 8 - 2 a = 0

20=(5^2sqrt(p))/5

20 = \frac{5 ^{2} p}{5}

x^{- \frac{2}{5}} = \frac{1}{16}