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Beliebt Algebra >

8k^6+15k^3-2=0

Lösung

8 k^{6} + 15 k^{3} - 2 = 0

Lösung

k = \frac{1}{2}, k = - \frac{1}{4} + \frac{3}{4} i, k = - \frac{1}{4} - \frac{3}{4} i, k = - 32, k = \frac{3 2}{2} - i \frac{3 2 3}{2}, k = \frac{3 2}{2} + i \frac{3 2 3}{2}

Schritte zur Lösung

8 k^{6} + 15 k^{3} - 2 = 0

Schreibe die Gleichung um mit

u = k^{3}

und

u^{2} = k^{6}

8 u^{2} + 15 u - 2 = 0

Löse

8 u^{2} + 15 u - 2 = 0 : u = \frac{1}{8}, u = - 2

u = \frac{1}{8}, u = - 2

Setze

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

löse für

k

Löse

k^{3} = \frac{1}{8} : k = \frac{1}{2}, k = - \frac{1}{4} + \frac{3}{4} i, k = - \frac{1}{4} - \frac{3}{4} i

Löse

k^{3} = - 2 : k = - 32, k = \frac{3 2}{2} - i \frac{3 2 3}{2}, k = \frac{3 2}{2} + i \frac{3 2 3}{2}

Die Lösungen sind

k = \frac{1}{2}, k = - \frac{1}{4} + \frac{3}{4} i, k = - \frac{1}{4} - \frac{3}{4} i, k = - 32, k = \frac{3 2}{2} - i \frac{3 2 3}{2}, k = \frac{3 2}{2} + i \frac{3 2 3}{2}

Graph

Beliebte Beispiele

((x-1)/3)^3=(1/5)^6

(\frac{x - 1}{3})^{3} = (\frac{1}{5})^{6}

(x+1)^3+(x+2)^3+(x+3)^3+(x+4)^3=(x+5)^3

(x + 1)^{3} + (x + 2)^{3} + (x + 3)^{3} + (x + 4)^{3} = (x + 5)^{3}

x^{3} - 3 x - 1 = 0

x^3-2x^2-9x+18=0

x^{3} - 2 x^{2} - 9 x + 18 = 0

2 x^{3} - 3 x^{2} = 9