solvefor x,x^3=6y

Lösung

löse nach

x, x^{3} = 6 y

x = 3 6 y, x = - \frac{3 3 3 y}{( 3 2 ) ^{2}} + \frac{6 3 ^{5} 3 y}{( 3 2 ) ^{2}} i, x = - \frac{3 3 3 y}{( 3 2 ) ^{2}} - \frac{6 3 ^{5} 3 y}{( 3 2 ) ^{2}} i

Schritte zur Lösung

x^{3} = 6 y

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 6 y, x = 3 6 y \frac{- 1 + 3 i}{2}, x = 3 6 y \frac{- 1 - 3 i}{2}

Vereinfache

3 6 y \frac{- 1 + 3 i}{2} : - \frac{3 3 3 y}{( 3 2 ) ^{2}} + \frac{6 3 ^{5} 3 y}{( 3 2 ) ^{2}} i

Vereinfache

3 6 y \frac{- 1 - 3 i}{2} : - \frac{3 3 3 y}{( 3 2 ) ^{2}} - \frac{6 3 ^{5} 3 y}{( 3 2 ) ^{2}} i

x = 3 6 y, x = - \frac{3 3 3 y}{( 3 2 ) ^{2}} + \frac{6 3 ^{5} 3 y}{( 3 2 ) ^{2}} i, x = - \frac{3 3 3 y}{( 3 2 ) ^{2}} - \frac{6 3 ^{5} 3 y}{( 3 2 ) ^{2}} i

x^{4} - 6 x^{3} + 7 x^{2} + 6 x - 8 = 0

(2 x - 1)^{6} = 64

x^{4} + 2 x^{2} - 24 = 0

16 = x^{4}

8 x^{3} + 4 x^{2} - 50 x - 25 = 0