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Beliebt Algebra >

3x^6+4x^4+4x^2+1=0

Lösung

3 x^{6} + 4 x^{4} + 4 x^{2} + 1 = 0

Lösung

x = \frac{1}{3} i, x = - \frac{1}{3} i, x = \frac{1}{2} + \frac{3}{2} i, x = - \frac{1}{2} - \frac{3}{2} i, x = \frac{1}{2} - \frac{3}{2} i, x = - \frac{1}{2} + \frac{3}{2} i

Schritte zur Lösung

3 x^{6} + 4 x^{4} + 4 x^{2} + 1 = 0

Schreibe die Gleichung um mit

u = x^{2}, u^{2} = x^{4}

und

u^{3} = x^{6}

3 u^{3} + 4 u^{2} + 4 u + 1 = 0

Löse

3 u^{3} + 4 u^{2} + 4 u + 1 = 0 : u = - \frac{1}{3}, u = - \frac{1}{2} + i \frac{3}{2}, u = - \frac{1}{2} - i \frac{3}{2}

u = - \frac{1}{3}, u = - \frac{1}{2} + i \frac{3}{2}, u = - \frac{1}{2} - i \frac{3}{2}

Setze

u = x^{2} w i e d er e in,

löse für

x

Löse

x^{2} = - \frac{1}{3} : x = \frac{1}{3} i, x = - \frac{1}{3} i

Löse

x^{2} = - \frac{1}{2} + i \frac{3}{2} : x = \frac{1}{2} + \frac{3}{2} i, x = - \frac{1}{2} - \frac{3}{2} i

Löse

x^{2} = - \frac{1}{2} - i \frac{3}{2} : x = \frac{1}{2} - \frac{3}{2} i, x = - \frac{1}{2} + \frac{3}{2} i

Die Lösungen sind

x = \frac{1}{3} i, x = - \frac{1}{3} i, x = \frac{1}{2} + \frac{3}{2} i, x = - \frac{1}{2} - \frac{3}{2} i, x = \frac{1}{2} - \frac{3}{2} i, x = - \frac{1}{2} + \frac{3}{2} i

Graph

Beliebte Beispiele

n^3-n^2+15n-500=0

n^{3} - n^{2} + 15 n - 500 = 0

2 x^{4} - x^{2} = 0

x^{6} + 12 x^{3} + 32 = 0

solvefor x,y^2=cx^4-2

so l v e f or x, y^{2} = c x^{4} - 2

x^{16} - 1 = 0