solvefor y,y^3=x^2

Lösung

löse nach

y, y^{3} = x^{2}

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

Schritte zur Lösung

y^{3} = x^{2}

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}

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

Vereinfache

3 x^{2} \frac{- 1 + 3 i}{2} : - \frac{3 x ^{2}}{2} + \frac{3 x ^{2} 3}{2} i

Vereinfache

3 x^{2} \frac{- 1 - 3 i}{2} : - \frac{3 x ^{2}}{2} - \frac{3 x ^{2} 3}{2} i

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

x^{5} = 25 x^{3}

x^{6} + 56 x^{3} - 512 = 0

2 x^{3} - 3 x^{2} + 8 x - 12 = 0

- 2 (3 x - 1) (x^{2} - 9) = 0

12 k^{3} - 48 k^{2} + 12 k + 72 = 0