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Beliebt Algebra >

x^6-7x^3+12=0

Lösung

x^{6} - 7 x^{3} + 12 = 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 = 33, x = - 33 \frac{1}{2} + 33 \frac{3}{2} i, x = - 33 \frac{1}{2} - 33 \frac{3}{2} i

Schritte zur Lösung

x^{6} - 7 x^{3} + 12 = 0

Schreibe die Gleichung um mit

u = x^{3}

und

u^{2} = x^{6}

u^{2} - 7 u + 12 = 0

Löse

u^{2} - 7 u + 12 = 0 : u = 4, u = 3

u = 4, u = 3

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} = 3 : x = 33, x = - 33 \frac{1}{2} + 33 \frac{3}{2} i, x = - 33 \frac{1}{2} - 33 \frac{3}{2} i

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 = 33, x = - 33 \frac{1}{2} + 33 \frac{3}{2} i, x = - 33 \frac{1}{2} - 33 \frac{3}{2} i

Graph

Beliebte Beispiele

8x^4-96x^3+320x^2+588x-1764=0

8 x^{4} - 96 x^{3} + 320 x^{2} + 588 x - 1764 = 0

m^{4} = 625

5x^3+4x^2-12x=0

5 x^{3} + 4 x^{2} - 12 x = 0

x^{5} - 16 x = 0

x^{3} = - 27