12x-6x^2+3x^4=6x^3+2x-x^4

Lösung

12 x - 6 x^{2} + 3 x^{4} = 6 x^{3} + 2 x - x^{4}

x = 0, x \approx - 1.26116 \dots

Schritte zur Lösung

12 x - 6 x^{2} + 3 x^{4} = 6 x^{3} + 2 x - x^{4}

Subtrahiere

6 x^{3} + 2 x - x^{4}

von beiden Seiten

12 x - 6 x^{2} + 3 x^{4} - (6 x^{3} + 2 x - x^{4}) = 6 x^{3} + 2 x - x^{4} - (6 x^{3} + 2 x - x^{4})

Vereinfache

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

Faktorisiere

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

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

2 x^{3} - 3 x^{2} - 3 x + 5 = 0 : x \approx - 1.26116 \dots

Die Lösungen sind

x = 0, x \approx - 1.26116 \dots

4 x^{3} + 56 x^{2} + 132 x = 0

125 t^{10} - 3 t^{7} = 0

- 3 x^{3} + 40 x^{2} - 90 x + 150 = 0

x^{3} - 11 x^{2} - 16 x + 176 = 0

12 x^{3} + 24 x^{2} - 96 x = 0