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Beliebt Algebra >

x^6+x^3-20=0

Lösung

x^{6} + x^{3} - 20 = 0

Lösung

x = 34, x = - 34 \frac{1}{2} + 34 \frac{3}{2} i, x = - 34 \frac{1}{2} - 34 \frac{3}{2} i, x = - 35, x = - \frac{3 5 ( - 1 + 3 i )}{2}, x = - \frac{3 5 ( - 1 - 3 i )}{2}

Schritte zur Lösung

x^{6} + x^{3} - 20 = 0

Schreibe die Gleichung um mit

u = x^{3}

und

u^{2} = x^{6}

u^{2} + u - 20 = 0

Löse

u^{2} + u - 20 = 0 : u = 4, u = - 5

u = 4, u = - 5

Setze

u = x^{3} w i e d er e in,

löse für

x

Löse

x^{3} = 4 : x = 34, x = - 34 \frac{1}{2} + 34 \frac{3}{2} i, x = - 34 \frac{1}{2} - 34 \frac{3}{2} i

Löse

x^{3} = - 5 : x = - 35, x = - \frac{3 5 ( - 1 + 3 i )}{2}, x = - \frac{3 5 ( - 1 - 3 i )}{2}

Die Lösungen sind

x = 34, x = - 34 \frac{1}{2} + 34 \frac{3}{2} i, x = - 34 \frac{1}{2} - 34 \frac{3}{2} i, x = - 35, x = - \frac{3 5 ( - 1 + 3 i )}{2}, x = - \frac{3 5 ( - 1 - 3 i )}{2}

Graph

Beliebte Beispiele

x (x + 1) (x - 1) = 0

x^{3} = \frac{64}{27}

(x + 1)^{3} = 27

x^3-6x^2+9x-1=0

x^{3} - 6 x^{2} + 9 x - 1 = 0

-a^3+24a^2-180a+432=0

- a^{3} + 24 a^{2} - 180 a + 432 = 0