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Beliebt Algebra >

((a^2)/3)^2+(a)^2=50

Lösung

(\frac{a ^{2}}{3})^{2} + (a)^{2} = 50

Lösung

a = \frac{- 9 + 3 209}{2}, a = - \frac{- 9 + 3 209}{2}, a = \frac{- 9 - 3 209}{2}, a = - \frac{- 9 - 3 209}{2}

Schritte zur Lösung

(\frac{a ^{2}}{3})^{2} + a^{2} = 50

Schreibe

(\frac{a ^{2}}{3})^{2} + a^{2}

um:

\frac{a ^{4}}{9} + a^{2}

\frac{a ^{4}}{9} + a^{2} = 50

Verschiebe

50

auf die linke Seite

\frac{a ^{4}}{9} + a^{2} - 50 = 0

Schreibe in der Standard Form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

\frac{1 \cdot a ^{4}}{9} + a^{2} - 50 = 0

Schreibe die Gleichung um mit

u = a^{2}

und

u^{2} = a^{4}

\frac{1 \cdot u ^{2}}{9} + u - 50 = 0

Löse

\frac{1 \cdot u ^{2}}{9} + u - 50 = 0 : u = \frac{- 9 + 3 209}{2}, u = \frac{- 9 - 3 209}{2}

u = \frac{- 9 + 3 209}{2}, u = \frac{- 9 - 3 209}{2}

Setze

u = a^{2} w i e d er e in,

löse für

a

Löse

a^{2} = \frac{- 9 + 3 209}{2} : a = \frac{- 9 + 3 209}{2}, a = - \frac{- 9 + 3 209}{2}

Löse

a^{2} = \frac{- 9 - 3 209}{2} : a = \frac{- 9 - 3 209}{2}, a = - \frac{- 9 - 3 209}{2}

Die Lösungen sind

a = \frac{- 9 + 3 209}{2}, a = - \frac{- 9 + 3 209}{2}, a = \frac{- 9 - 3 209}{2}, a = - \frac{- 9 - 3 209}{2}

Graph

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