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Beliebt Algebra >

x^6-14x^3+40=0

Lösung

x^{6} - 14 x^{3} + 40 = 0

Lösung

x = 310, x = - 310 \frac{1}{2} + 310 \frac{3}{2} i, x = - 310 \frac{1}{2} - 310 \frac{3}{2} i, x = 34, x = - 34 \frac{1}{2} + 34 \frac{3}{2} i, x = - 34 \frac{1}{2} - 34 \frac{3}{2} i

Schritte zur Lösung

x^{6} - 14 x^{3} + 40 = 0

Schreibe die Gleichung um mit

u = x^{3}

und

u^{2} = x^{6}

u^{2} - 14 u + 40 = 0

Löse

u^{2} - 14 u + 40 = 0 : u = 10, u = 4

u = 10, u = 4

Setze

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

löse für

x

Löse

x^{3} = 10 : x = 310, x = - 310 \frac{1}{2} + 310 \frac{3}{2} i, x = - 310 \frac{1}{2} - 310 \frac{3}{2} i

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

Die Lösungen sind

x = 310, x = - 310 \frac{1}{2} + 310 \frac{3}{2} i, x = - 310 \frac{1}{2} - 310 \frac{3}{2} i, x = 34, x = - 34 \frac{1}{2} + 34 \frac{3}{2} i, x = - 34 \frac{1}{2} - 34 \frac{3}{2} i

Graph

Beliebte Beispiele

solvefor x,x^3+y^3=6

so l v e f or x, x^{3} + y^{3} = 6

3 x^{5} - 5 x^{3} = 0

60x^5+120x^4+60x^3=0

60 x^{5} + 120 x^{4} + 60 x^{3} = 0

6 x^{4} = 48 x

x^{2} - x^{5} + 6 = 0