solvefor y,9x^5+6y^3=5x+10x^6

Lösung

löse nach

y, 9 x^{5} + 6 y^{3} = 5 x + 10 x^{6}

y = 3 \frac{5 x + 10 x ^{6} - 9 x ^{5}}{6}, y = - \frac{3 \frac{5 x + 10 x ^{6} - 9 x ^{5}}{6}}{2} + \frac{3 \frac{5 x + 10 x ^{6} - 9 x ^{5}}{6} 3}{2} i, y = - \frac{3 \frac{5 x + 10 x ^{6} - 9 x ^{5}}{6}}{2} - \frac{3 \frac{5 x + 10 x ^{6} - 9 x ^{5}}{6} 3}{2} i

Schritte zur Lösung

9 x^{5} + 6 y^{3} = 5 x + 10 x^{6}

Verschiebe

9 x^{5}

auf die rechte Seite

6 y^{3} = 5 x + 10 x^{6} - 9 x^{5}

Teile beide Seiten durch

6

y^{3} = \frac{5 x + 10 x ^{6} - 9 x ^{5}}{6}

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 \frac{5 x + 10 x ^{6} - 9 x ^{5}}{6}, y = 3 \frac{5 x + 10 x ^{6} - 9 x ^{5}}{6} \frac{- 1 + 3 i}{2}, y = 3 \frac{5 x + 10 x ^{6} - 9 x ^{5}}{6} \frac{- 1 - 3 i}{2}

Vereinfache

3 \frac{5 x + 10 x ^{6} - 9 x ^{5}}{6} \frac{- 1 + 3 i}{2} : - \frac{3 \frac{5 x + 10 x ^{6} - 9 x ^{5}}{6}}{2} + \frac{3 \frac{5 x + 10 x ^{6} - 9 x ^{5}}{6} 3}{2} i

Vereinfache

3 \frac{5 x + 10 x ^{6} - 9 x ^{5}}{6} \frac{- 1 - 3 i}{2} : - \frac{3 \frac{5 x + 10 x ^{6} - 9 x ^{5}}{6}}{2} - \frac{3 \frac{5 x + 10 x ^{6} - 9 x ^{5}}{6} 3}{2} i

y = 3 \frac{5 x + 10 x ^{6} - 9 x ^{5}}{6}, y = - \frac{3 \frac{5 x + 10 x ^{6} - 9 x ^{5}}{6}}{2} + \frac{3 \frac{5 x + 10 x ^{6} - 9 x ^{5}}{6} 3}{2} i, y = - \frac{3 \frac{5 x + 10 x ^{6} - 9 x ^{5}}{6}}{2} - \frac{3 \frac{5 x + 10 x ^{6} - 9 x ^{5}}{6} 3}{2} i

x^{4} + 6 x^{3} - 5 x^{2} - 24 x + 4 = 0

x^{4} + 6 x^{3} + 8 x^{2} - 6 x - 9 = 0

x^{4} - 9 x^{3} + 27 x^{2} - 27 x = 0

x^{3} + 3 x^{2} - 18 x - 40 = 0

roo t s x^{4} + 2 x^{2} - x + 8