de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Algebra >

z^6-12=0

Lösung

z^{6} - 12 = 0

Lösung

z = 312, z = - 312, z = 0.75654 \dots + \frac{3 ^{\frac{5}{6}}}{1.51308 \dots 3 2} i, z = - 0.75654 \dots - \frac{3 ^{\frac{5}{6}}}{1.51308 \dots 3 2} i, z = 0.75654 \dots - \frac{3 ^{\frac{5}{6}}}{1.51308 \dots 3 2} i, z = - 0.75654 \dots + \frac{3 ^{\frac{5}{6}}}{1.51308 \dots 3 2} i

Schritte zur Lösung

z^{6} - 12 = 0

Verschiebe

12

auf die rechte Seite

z^{6} = 12

Schreibe die Gleichung um mit

u = z^{2}

und

u^{3} = z^{6}

u^{3} = 12

Löse

u^{3} = 12 : u = 312, u = 312 \frac{- 1 + 3 i}{2}, u = 312 \frac{- 1 - 3 i}{2}

u = 312, u = 312 \frac{- 1 + 3 i}{2}, u = 312 \frac{- 1 - 3 i}{2}

Setze

u = z^{2} w i e d er e in,

löse für

z

Löse

z^{2} = 312 : z = 312, z = - 312

Löse

z^{2} = 312 \frac{- 1 + 3 i}{2} : z = 0.75654 \dots + \frac{3 ^{\frac{5}{6}}}{1.51308 \dots 3 2} i, z = - 0.75654 \dots - \frac{3 ^{\frac{5}{6}}}{1.51308 \dots 3 2} i

Löse

z^{2} = 312 \frac{- 1 - 3 i}{2} : z = 0.75654 \dots - \frac{3 ^{\frac{5}{6}}}{1.51308 \dots 3 2} i, z = - 0.75654 \dots + \frac{3 ^{\frac{5}{6}}}{1.51308 \dots 3 2} i

Die Lösungen sind

z = 312, z = - 312, z = 0.75654 \dots + \frac{3 ^{\frac{5}{6}}}{1.51308 \dots 3 2} i, z = - 0.75654 \dots - \frac{3 ^{\frac{5}{6}}}{1.51308 \dots 3 2} i, z = 0.75654 \dots - \frac{3 ^{\frac{5}{6}}}{1.51308 \dots 3 2} i, z = - 0.75654 \dots + \frac{3 ^{\frac{5}{6}}}{1.51308 \dots 3 2} i

Graph

Beliebte Beispiele

-λ^3+12λ^2-21λ+10=0

- λ^{3} + 12 λ^{2} - 21 λ + 10 = 0

x^4+2x^3-11x^2-12x+36=0

x^{4} + 2 x^{3} - 11 x^{2} - 12 x + 36 = 0

x^{2} + x^{10} = 0

4 \cdot x^{3} = 32

solvefor x,xx^2+y^2=0

so l v e f or x, x x^{2} + y^{2} = 0