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Beliebt Algebra >

solvefor x,VV-2GR-KV V/M =x^2-K(x^2)/M-2KV x/M

Lösung

löse nach

x, VV - 2 \cdot G \cdot R - K V \frac{V}{M} = x^{2} - K \cdot \frac{x ^{2}}{M} - 2 \cdot K V \frac{x}{M}

Lösung

x = \frac{V K + M ^{2} V ^{2} + 2 V ^{2} K ^{2} - 2 M V ^{2} K + 2 MRG K - 2 M ^{2} RG}{M - K}, x = \frac{V K - M ^{2} V ^{2} + 2 V ^{2} K ^{2} - 2 M V ^{2} K + 2 MRG K - 2 M ^{2} RG}{M - K}; 1 - \frac{K}{M} \neq = 0

Schritte zur Lösung

VV - 2 GR - K V \frac{V}{M} = x^{2} - K \frac{x ^{2}}{M} - 2 K V \frac{x}{M}

Schreibe

VV - 2 GR - K V \frac{V}{M}

um:

V^{2} - 2 RG - \frac{V ^{2} K}{M}

Schreibe

x^{2} - K \frac{x ^{2}}{M} - 2 K V \frac{x}{M}

um:

x^{2} - \frac{x ^{2} K}{M} - \frac{2 x V K}{M}

V^{2} - 2 RG - \frac{V ^{2} K}{M} = x^{2} - \frac{x ^{2} K}{M} - \frac{2 x V K}{M}

Tausche die Seiten

x^{2} - \frac{x ^{2} K}{M} - \frac{2 x V K}{M} = V^{2} - 2 RG - \frac{V ^{2} K}{M}

Verschiebe

\frac{V ^{2} K}{M}

auf die linke Seite

x^{2} + \frac{- x ^{2} K - 2 x V K + V ^{2} K}{M} = V^{2} - 2 RG

Verschiebe

2 RG

auf die linke Seite

x^{2} + \frac{- x ^{2} K - 2 x V K + V ^{2} K}{M} + 2 RG = V^{2}

Verschiebe

V^{2}

auf die linke Seite

x^{2} + \frac{- x ^{2} K - 2 x V K + V ^{2} K}{M} + 2 RG - V^{2} = 0

Schreibe in der Standard Form

a x^{2} + b x + c = 0

(1 - \frac{K}{M}) x^{2} - \frac{2 V K x}{M} + \frac{V ^{2} K}{M} + 2 RG - V^{2} = 0

Löse mit der quadratischen Formel

x_{1, 2} = \frac{- ( - \frac{2 V K}{M} ) \pm ( - \frac{2 V K}{M} ) ^{2} - 4 ( 1 - \frac{K}{M} ) ( \frac{V ^{2} K}{M} + 2 RG - V ^{2} )}{2 ( 1 - \frac{K}{M} )}

Vereinfache

(- \frac{2 V K}{M})^{2} - 4 (1 - \frac{K}{M}) (\frac{V ^{2} K}{M} + 2 RG - V^{2}) : \frac{2 M ^{2} V ^{2} + 2 V ^{2} K ^{2} - 2 M V ^{2} K - 2 M ^{2} RG + 2 MRG K}{M}

x_{1, 2} = \frac{- ( - \frac{2 V K}{M} ) \pm \frac{2 M ^{2} V ^{2} + 2 V ^{2} K ^{2} - 2 M V ^{2} K - 2 M ^{2} RG + 2 MRG K}{M}}{2 ( 1 - \frac{K}{M} )}; 1 - \frac{K}{M} \neq = 0

Trenne die Lösungen

x_{1} = \frac{- ( - \frac{2 V K}{M} ) + \frac{2 M ^{2} V ^{2} + 2 V ^{2} K ^{2} - 2 M V ^{2} K - 2 M ^{2} RG + 2 MRG K}{M}}{2 ( 1 - \frac{K}{M} )}, x_{2} = \frac{- ( - \frac{2 V K}{M} ) - \frac{2 M ^{2} V ^{2} + 2 V ^{2} K ^{2} - 2 M V ^{2} K - 2 M ^{2} RG + 2 MRG K}{M}}{2 ( 1 - \frac{K}{M} )}

x = \frac{- ( - \frac{2 V K}{M} ) + \frac{2 M ^{2} V ^{2} + 2 V ^{2} K ^{2} - 2 M V ^{2} K - 2 M ^{2} RG + 2 MRG K}{M}}{2 ( 1 - \frac{K}{M} )} : \frac{V K + M ^{2} V ^{2} + 2 V ^{2} K ^{2} - 2 M V ^{2} K + 2 MRG K - 2 M ^{2} RG}{M - K}

x = \frac{- ( - \frac{2 V K}{M} ) - \frac{2 M ^{2} V ^{2} + 2 V ^{2} K ^{2} - 2 M V ^{2} K - 2 M ^{2} RG + 2 MRG K}{M}}{2 ( 1 - \frac{K}{M} )} : \frac{V K - M ^{2} V ^{2} + 2 V ^{2} K ^{2} - 2 M V ^{2} K + 2 MRG K - 2 M ^{2} RG}{M - K}

Die Lösungen für die quadratische Gleichung sind:

x = \frac{V K + M ^{2} V ^{2} + 2 V ^{2} K ^{2} - 2 M V ^{2} K + 2 MRG K - 2 M ^{2} RG}{M - K}, x = \frac{V K - M ^{2} V ^{2} + 2 V ^{2} K ^{2} - 2 M V ^{2} K + 2 MRG K - 2 M ^{2} RG}{M - K}; 1 - \frac{K}{M} \neq = 0

Graph

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