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Beliebt Algebra >

solvefor t,f=(t-3)u^2(t)-(t-2)u^3(t)

Lösung

löse nach

t, f = (t - 3) u^{2} (t) - (t - 2) u^{3} (t)

Lösung

t = \frac{3 u ^{2} - 2 u ^{3} + ( - 3 u ^{2} + 2 u ^{3} ) ^{2} + 4 f ( u ^{2} - u ^{3} )}{2 ( u ^{2} - u ^{3} )}, t = \frac{3 u ^{2} - 2 u ^{3} - ( - 3 u ^{2} + 2 u ^{3} ) ^{2} + 4 f ( u ^{2} - u ^{3} )}{2 ( u ^{2} - u ^{3} )}; u \neq = 0, u \neq = 1

Schritte zur Lösung

f = (t - 3) u^{2} (t) - (t - 2) u^{3} (t)

Schreibe

(t - 3) u^{2} (t) - (t - 2) u^{3} (t)

um:

t^{2} u^{2} - 3 t u^{2} - t^{2} u^{3} + 2 t u^{3}

f = t^{2} u^{2} - 3 t u^{2} - t^{2} u^{3} + 2 t u^{3}

Tausche die Seiten

t^{2} u^{2} - 3 t u^{2} - t^{2} u^{3} + 2 t u^{3} = f

Verschiebe

f

auf die linke Seite

t^{2} u^{2} - 3 t u^{2} - t^{2} u^{3} + 2 t u^{3} - f = 0

Schreibe in der Standard Form

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

(u^{2} - u^{3}) t^{2} + (- 3 u^{2} + 2 u^{3}) t - f = 0

Löse mit der quadratischen Formel

t_{1, 2} = \frac{- ( - 3 u ^{2} + 2 u ^{3} ) \pm ( - 3 u ^{2} + 2 u ^{3} ) ^{2} - 4 ( u ^{2} - u ^{3} ) ( - f )}{2 ( u ^{2} - u ^{3} )}

Vereinfache

(- 3 u^{2} + 2 u^{3})^{2} - 4 (u^{2} - u^{3}) (- f) : (- 3 u^{2} + 2 u^{3})^{2} + 4 f (u^{2} - u^{3})

t_{1, 2} = \frac{- ( - 3 u ^{2} + 2 u ^{3} ) \pm ( - 3 u ^{2} + 2 u ^{3} ) ^{2} + 4 f ( u ^{2} - u ^{3} )}{2 ( u ^{2} - u ^{3} )}; u \neq = 0, u \neq = 1

Trenne die Lösungen

t_{1} = \frac{- ( - 3 u ^{2} + 2 u ^{3} ) + ( - 3 u ^{2} + 2 u ^{3} ) ^{2} + 4 f ( u ^{2} - u ^{3} )}{2 ( u ^{2} - u ^{3} )}, t_{2} = \frac{- ( - 3 u ^{2} + 2 u ^{3} ) - ( - 3 u ^{2} + 2 u ^{3} ) ^{2} + 4 f ( u ^{2} - u ^{3} )}{2 ( u ^{2} - u ^{3} )}

t = \frac{- ( - 3 u ^{2} + 2 u ^{3} ) + ( - 3 u ^{2} + 2 u ^{3} ) ^{2} + 4 f ( u ^{2} - u ^{3} )}{2 ( u ^{2} - u ^{3} )} : \frac{3 u ^{2} - 2 u ^{3} + ( - 3 u ^{2} + 2 u ^{3} ) ^{2} + 4 f ( u ^{2} - u ^{3} )}{2 ( u ^{2} - u ^{3} )}

t = \frac{- ( - 3 u ^{2} + 2 u ^{3} ) - ( - 3 u ^{2} + 2 u ^{3} ) ^{2} + 4 f ( u ^{2} - u ^{3} )}{2 ( u ^{2} - u ^{3} )} : \frac{3 u ^{2} - 2 u ^{3} - ( - 3 u ^{2} + 2 u ^{3} ) ^{2} + 4 f ( u ^{2} - u ^{3} )}{2 ( u ^{2} - u ^{3} )}

Die Lösungen für die quadratische Gleichung sind:

t = \frac{3 u ^{2} - 2 u ^{3} + ( - 3 u ^{2} + 2 u ^{3} ) ^{2} + 4 f ( u ^{2} - u ^{3} )}{2 ( u ^{2} - u ^{3} )}, t = \frac{3 u ^{2} - 2 u ^{3} - ( - 3 u ^{2} + 2 u ^{3} ) ^{2} + 4 f ( u ^{2} - u ^{3} )}{2 ( u ^{2} - u ^{3} )}; u \neq = 0, u \neq = 1

Graph

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