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Beliebt Algebra >

solvefor x,x^3y(p-1)+p^2e^2y=0

Lösung

löse nach

x, x^{3} y (p - 1) + p^{2} e^{2} y = 0

Lösung

x = - 3 \frac{e ^{2} p ^{2}}{p - 1}, x = \frac{( - 1 + p ) ^{\frac{2}{3}} 3 e ^{2} p ^{2}}{- 2 + 2 p} - i \frac{3 ( - 1 + p ) ^{\frac{2}{3}} 3 e ^{2} p ^{2}}{- 2 + 2 p}, x = \frac{( - 1 + p ) ^{\frac{2}{3}} 3 e ^{2} p ^{2}}{- 2 + 2 p} + i \frac{3 ( - 1 + p ) ^{\frac{2}{3}} 3 e ^{2} p ^{2}}{- 2 + 2 p}; p \neq = 1

Schritte zur Lösung

x^{3} y (p - 1) + p^{2} e^{2} y = 0

Verschiebe

p^{2} e^{2} y

auf die rechte Seite

x^{3} y (p - 1) = - e^{2} p^{2} y

Teile beide Seiten durch

y (p - 1); p \neq = 1

x^{3} = - \frac{e ^{2} p ^{2}}{p - 1}; p \neq = 1

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 - \frac{e ^{2} p ^{2}}{p - 1}, x = 3 - \frac{e ^{2} p ^{2}}{p - 1} \frac{- 1 + 3 i}{2}, x = 3 - \frac{e ^{2} p ^{2}}{p - 1} \frac{- 1 - 3 i}{2}; p \neq = 1

Vereinfache

3 - \frac{e ^{2} p ^{2}}{p - 1} : - 3 \frac{e ^{2} p ^{2}}{p - 1}

Vereinfache

3 - \frac{e ^{2} p ^{2}}{p - 1} \frac{- 1 + 3 i}{2} : \frac{( - 1 + p ) ^{\frac{2}{3}} 3 e ^{2} p ^{2}}{- 2 + 2 p} - i \frac{3 ( - 1 + p ) ^{\frac{2}{3}} 3 e ^{2} p ^{2}}{- 2 + 2 p}

Vereinfache

3 - \frac{e ^{2} p ^{2}}{p - 1} \frac{- 1 - 3 i}{2} : \frac{( - 1 + p ) ^{\frac{2}{3}} 3 e ^{2} p ^{2}}{- 2 + 2 p} + i \frac{3 ( - 1 + p ) ^{\frac{2}{3}} 3 e ^{2} p ^{2}}{- 2 + 2 p}

x = - 3 \frac{e ^{2} p ^{2}}{p - 1}, x = \frac{( - 1 + p ) ^{\frac{2}{3}} 3 e ^{2} p ^{2}}{- 2 + 2 p} - i \frac{3 ( - 1 + p ) ^{\frac{2}{3}} 3 e ^{2} p ^{2}}{- 2 + 2 p}, x = \frac{( - 1 + p ) ^{\frac{2}{3}} 3 e ^{2} p ^{2}}{- 2 + 2 p} + i \frac{3 ( - 1 + p ) ^{\frac{2}{3}} 3 e ^{2} p ^{2}}{- 2 + 2 p}; p \neq = 1

Graph

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