x^6+28x^3+16=0

Lösung

x^{6} + 28 x^{3} + 16 = 0

x = 3 2 (35 - 7), x = - 3 2 (35 - 7) \frac{1}{2} + 3 2 (35 - 7) \frac{3}{2} i, x = - 3 2 (35 - 7) \frac{1}{2} - 3 2 (35 - 7) \frac{3}{2} i, x = 32 3 - 7 - 35, x = - 3 \frac{- 7 - 3 5}{4} + i \frac{3 2 3 3 - 7 - 3 5}{2}, x = - 3 \frac{- 7 - 3 5}{4} - i \frac{3 2 3 3 - 7 - 3 5}{2}

Schritte zur Lösung

x^{6} + 28 x^{3} + 16 = 0

Schreibe die Gleichung um mit

u = x^{3}

und

u^{2} = x^{6}

u^{2} + 28 u + 16 = 0

Löse

u^{2} + 28 u + 16 = 0 : u = 2 (35 - 7), u = - 2 (7 + 35)

u = 2 (35 - 7), u = - 2 (7 + 35)

Setze

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

löse für

x

Löse

x^{3} = 2 (35 - 7) : x = 3 2 (35 - 7), x = - 3 2 (35 - 7) \frac{1}{2} + 3 2 (35 - 7) \frac{3}{2} i, x = - 3 2 (35 - 7) \frac{1}{2} - 3 2 (35 - 7) \frac{3}{2} i

Löse

x^{3} = - 2 (7 + 35) : x = 32 3 - 7 - 35, x = - 3 \frac{- 7 - 3 5}{4} + i \frac{3 2 3 3 - 7 - 3 5}{2}, x = - 3 \frac{- 7 - 3 5}{4} - i \frac{3 2 3 3 - 7 - 3 5}{2}

Die Lösungen sind

x = 3 2 (35 - 7), x = - 3 2 (35 - 7) \frac{1}{2} + 3 2 (35 - 7) \frac{3}{2} i, x = - 3 2 (35 - 7) \frac{1}{2} - 3 2 (35 - 7) \frac{3}{2} i, x = 32 3 - 7 - 35, x = - 3 \frac{- 7 - 3 5}{4} + i \frac{3 2 3 3 - 7 - 3 5}{2}, x = - 3 \frac{- 7 - 3 5}{4} - i \frac{3 2 3 3 - 7 - 3 5}{2}

(x + 2)^{3} = 0

x^{3} - 8 x^{2} - 4 x - 48 = 0

(0.0012 + x) (2 x)^{2} = 2.8 x 1 0^{- 7}

(x - 1) (2 x^{2} - 5 x + 2) = 0

(x - 1) (x^{2} + x + 1) = 0