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Beliebt Algebra >

x^6-2x^3-3=0

Lösung

x^{6} - 2 x^{3} - 3 = 0

Lösung

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

Schritte zur Lösung

x^{6} - 2 x^{3} - 3 = 0

Schreibe die Gleichung um mit

u = x^{3}

und

u^{2} = x^{6}

u^{2} - 2 u - 3 = 0

Löse

u^{2} - 2 u - 3 = 0 : u = 3, u = - 1

u = 3, u = - 1

Setze

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

löse für

x

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

Löse

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

Die Lösungen sind

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

Graph

Beliebte Beispiele

-x^3+6x^2-11x+6=0

- x^{3} + 6 x^{2} - 11 x + 6 = 0

z^4-6z^3+11z^2-46z+170=0

z^{4} - 6 z^{3} + 11 z^{2} - 46 z + 170 = 0

x^{4} - 5 x^{2} - 36 = 0

x^{4} - 13 x^{2} + 40 = 0

solvefor x,y^2=x^3

so l v e f or x, y^{2} = x^{3}