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Beliebt Algebra >

2x^6+7x^3-15=0

Lösung

2 x^{6} + 7 x^{3} - 15 = 0

Lösung

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

2 x^{6} + 7 x^{3} - 15 = 0

Schreibe die Gleichung um mit

u = x^{3}

und

u^{2} = x^{6}

2 u^{2} + 7 u - 15 = 0

Löse

2 u^{2} + 7 u - 15 = 0 : u = \frac{3}{2}, u = - 5

u = \frac{3}{2}, u = - 5

Setze

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

löse für

x

Löse

x^{3} = \frac{3}{2} : x = 3 \frac{3}{2}, x = - 3 \frac{3}{2} \frac{1}{2} + 3 \frac{3}{2} \frac{3}{2} i, x = - 3 \frac{3}{2} \frac{1}{2} - 3 \frac{3}{2} \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 = 3 \frac{3}{2}, x = - 3 \frac{3}{2} \frac{1}{2} + 3 \frac{3}{2} \frac{3}{2} i, x = - 3 \frac{3}{2} \frac{1}{2} - 3 \frac{3}{2} \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^3-4x+x(x+2)=0

x^{3} - 4 x + x (x + 2) = 0

x^{3} (x + 1) = - 6

solvefor x,-y=x^3

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

(1+0.8)=(1+x/(12))^3

(1 + 0.8) = (1 + \frac{x}{12})^{3}

2x^3+x^2-6x+7=0

2 x^{3} + x^{2} - 6 x + 7 = 0