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Beliebt Algebra >

(7.2+x^2)^2=x^2+2.67^2

Lösung

(7.2 + x^{2})^{2} = x^{2} + 2.6 7^{2}

Lösung

x = \frac{- 13.4 + 0.7156}{2}, x = - \frac{- 13.4 + 0.7156}{2}, x = \frac{- 13.4 - 0.7156}{2}, x = - \frac{- 13.4 - 0.7156}{2}

Schritte zur Lösung

(7.2 + x^{2})^{2} = x^{2} + 2.6 7^{2}

Schreibe

(7.2 + x^{2})^{2}

um:

51.84 + 14.4 x^{2} + x^{4}

Schreibe

x^{2} + 2.6 7^{2}

um:

x^{2} + 7.1289

51.84 + 14.4 x^{2} + x^{4} = x^{2} + 7.1289

Verschiebe

7.1289

auf die linke Seite

x^{4} + 14.4 x^{2} + 44.7111 = x^{2}

Verschiebe

x^{2}

auf die linke Seite

x^{4} + 13.4 x^{2} + 44.7111 = 0

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

u^{2} + 13.4 u + 44.7111 = 0

Löse

u^{2} + 13.4 u + 44.7111 = 0 : u = \frac{- 13.4 + 0.7156}{2}, u = \frac{- 13.4 - 0.7156}{2}

u = \frac{- 13.4 + 0.7156}{2}, u = \frac{- 13.4 - 0.7156}{2}

Setze

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

löse für

x

Löse

x^{2} = \frac{- 13.4 + 0.7156}{2} : x = \frac{- 13.4 + 0.7156}{2}, x = - \frac{- 13.4 + 0.7156}{2}

Löse

x^{2} = \frac{- 13.4 - 0.7156}{2} : x = \frac{- 13.4 - 0.7156}{2}, x = - \frac{- 13.4 - 0.7156}{2}

Die Lösungen sind

x = \frac{- 13.4 + 0.7156}{2}, x = - \frac{- 13.4 + 0.7156}{2}, x = \frac{- 13.4 - 0.7156}{2}, x = - \frac{- 13.4 - 0.7156}{2}

Graph

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