87=13*(1+x)^3

Lösung

87 = 13 \cdot (1 + x)^{3}

x = 3 \frac{87}{13} - 1, x = \frac{1 3 ^{\frac{2}{3}} ( - 3 87 - 2 3 13 )}{26} + i \frac{1 3 ^{\frac{2}{3}} \cdot 3 ^{\frac{5}{6}} 3 29}{26}, x = \frac{1 3 ^{\frac{2}{3}} ( - 3 87 - 2 3 13 )}{26} - i \frac{1 3 ^{\frac{2}{3}} \cdot 3 ^{\frac{5}{6}} 3 29}{26}

Schritte zur Lösung

87 = 13 (1 + x)^{3}

Tausche die Seiten

13 (1 + x)^{3} = 87

Teile beide Seiten durch

13

(1 + x)^{3} = \frac{87}{13}

Für

g^{3} (x) = f (a)

sind die Lösungen

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

Löse

1 + x = 3 \frac{87}{13} : x = 3 \frac{87}{13} - 1

Löse

1 + x = 3 \frac{87}{13} \frac{- 1 + 3 i}{2} : x = \frac{1 3 ^{\frac{2}{3}} ( - 3 87 - 2 3 13 )}{26} + i \frac{1 3 ^{\frac{2}{3}} \cdot 3 ^{\frac{5}{6}} 3 29}{26}

Löse

1 + x = 3 \frac{87}{13} \frac{- 1 - 3 i}{2} : x = \frac{1 3 ^{\frac{2}{3}} ( - 3 87 - 2 3 13 )}{26} - i \frac{1 3 ^{\frac{2}{3}} \cdot 3 ^{\frac{5}{6}} 3 29}{26}

Die Lösungen sind

x = 3 \frac{87}{13} - 1, x = \frac{1 3 ^{\frac{2}{3}} ( - 3 87 - 2 3 13 )}{26} + i \frac{1 3 ^{\frac{2}{3}} \cdot 3 ^{\frac{5}{6}} 3 29}{26}, x = \frac{1 3 ^{\frac{2}{3}} ( - 3 87 - 2 3 13 )}{26} - i \frac{1 3 ^{\frac{2}{3}} \cdot 3 ^{\frac{5}{6}} 3 29}{26}

186 = - 3 y^{3} - 6

4 x^{7} + 7 x^{4} + 5 x^{2} - 10 = x^{5}

- x^{3} + 27 x^{2} - 127 x - 699 = 0

- λ^{3} + 7 λ^{2} - 5 λ - 7 = 0

(x^{2} - 2 x)^{2} - (x^{2} - 2 x) = 2