solvefor y,5(y+1)^3+x^2=1

Lösung

löse nach

y, 5 (y + 1)^{3} + x^{2} = 1

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

Schritte zur Lösung

5 (y + 1)^{3} + x^{2} = 1

Verschiebe

x^{2}

auf die rechte Seite

5 (y + 1)^{3} = 1 - x^{2}

Teile beide Seiten durch

5

(y + 1)^{3} = \frac{1 - x ^{2}}{5}

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

y + 1 = 3 \frac{1 - x ^{2}}{5} : y = 3 \frac{1 - x ^{2}}{5} - 1

Löse

y + 1 = 3 \frac{1 - x ^{2}}{5} \frac{- 1 + 3 i}{2} : y = \frac{5 ^{\frac{2}{3}} ( - 3 1 - x ^{2} - 2 3 5 )}{10} + i \frac{5 ^{\frac{2}{3}} 3 3 1 - x ^{2}}{10}

Löse

y + 1 = 3 \frac{1 - x ^{2}}{5} \frac{- 1 - 3 i}{2} : y = \frac{5 ^{\frac{2}{3}} ( - 3 1 - x ^{2} - 2 3 5 )}{10} - i \frac{5 ^{\frac{2}{3}} 3 3 1 - x ^{2}}{10}

Die Lösungen sind

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

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

25 x^{4} - 65 x^{2} + 36 = 0

24 = r^{4}

so l v e f or x, x^{5} = y^{4}

so l v e f or x, x^{4} - 1 + y = 0