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Beliebt Algebra >

3x^4-15x^2+29=0

Lösung

3 x^{4} - 15 x^{2} + 29 = 0

Lösung

x = \frac{15 + 2 87}{2 3} + \frac{41}{2 15 + 2 87} i, x = - \frac{15 + 2 87}{2 3} - \frac{41}{2 15 + 2 87} i, x = \frac{15 + 2 87}{2 3} - \frac{41}{2 15 + 2 87} i, x = - \frac{15 + 2 87}{2 3} + \frac{41}{2 15 + 2 87} i

Schritte zur Lösung

3 x^{4} - 15 x^{2} + 29 = 0

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

3 u^{2} - 15 u + 29 = 0

Löse

3 u^{2} - 15 u + 29 = 0 : u = \frac{5}{2} + i \frac{123}{6}, u = \frac{5}{2} - i \frac{123}{6}

u = \frac{5}{2} + i \frac{123}{6}, u = \frac{5}{2} - i \frac{123}{6}

Setze

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

löse für

x

Löse

x^{2} = \frac{5}{2} + i \frac{123}{6} : x = \frac{15 + 2 87}{2 3} + \frac{41}{2 15 + 2 87} i, x = - \frac{15 + 2 87}{2 3} - \frac{41}{2 15 + 2 87} i

Löse

x^{2} = \frac{5}{2} - i \frac{123}{6} : x = \frac{15 + 2 87}{2 3} - \frac{41}{2 15 + 2 87} i, x = - \frac{15 + 2 87}{2 3} + \frac{41}{2 15 + 2 87} i

Die Lösungen sind

x = \frac{15 + 2 87}{2 3} + \frac{41}{2 15 + 2 87} i, x = - \frac{15 + 2 87}{2 3} - \frac{41}{2 15 + 2 87} i, x = \frac{15 + 2 87}{2 3} - \frac{41}{2 15 + 2 87} i, x = - \frac{15 + 2 87}{2 3} + \frac{41}{2 15 + 2 87} i

Graph

Beliebte Beispiele

a^{3} - 3 a^{2} = 240

s^5-s^3-s^2+1=0

s^{5} - s^{3} - s^{2} + 1 = 0

a^{5} = 7

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

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

x^{4} - 18 x^{2} + 32 = 0