bx^3=15

Lösung

b x^{3} = 15

x = 3 \frac{15}{b}, x = - \frac{3 \frac{15}{b}}{2} + \frac{3 \frac{15}{b} 3}{2} i, x = - \frac{3 \frac{15}{b}}{2} - \frac{3 \frac{15}{b} 3}{2} i; b \neq = 0

Schritte zur Lösung

b x^{3} = 15

Teile beide Seiten durch

b; b \neq = 0

x^{3} = \frac{15}{b}; b \neq = 0

Für

x^{3} = f (a)

sind die Lösungen

x = 3 f (a), 3 f (a) \frac{- 1 - 3 i}{2}, 3 f (a) \frac{- 1 + 3 i}{2}

x = 3 \frac{15}{b}, x = 3 \frac{15}{b} \frac{- 1 + 3 i}{2}, x = 3 \frac{15}{b} \frac{- 1 - 3 i}{2}; b \neq = 0

Vereinfache

3 \frac{15}{b} \frac{- 1 + 3 i}{2} : - \frac{3 \frac{15}{b}}{2} + \frac{3 \frac{15}{b} 3}{2} i

Vereinfache

3 \frac{15}{b} \frac{- 1 - 3 i}{2} : - \frac{3 \frac{15}{b}}{2} - \frac{3 \frac{15}{b} 3}{2} i

x = 3 \frac{15}{b}, x = - \frac{3 \frac{15}{b}}{2} + \frac{3 \frac{15}{b} 3}{2} i, x = - \frac{3 \frac{15}{b}}{2} - \frac{3 \frac{15}{b} 3}{2} i; b \neq = 0

x^{5} - 2 x^{4} - 5 x^{3} + 6 x^{2} = 0

4 x^{3} + 3 x^{2} + 64 x + 48 = 0

x^{5} = 1 0^{- 2}

so l v e f or x, x^{5} + 3 x^{2} + 2 x + 1 = 0

2 x = λ \cdot 4 x^{3}