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Beliebt Algebra >

solvefor x,x^2+(y-cbrt(x^2))^2=25

Lösung

löse nach

x, x^{2} + (y - c b r t (x^{2}))^{2} = 25

Lösung

x = \frac{- 1 + 2 c b yr t + 1 - 4 c b yr t + 100 c ^{2} b ^{2} r ^{2} t ^{2}}{2 c b r t}, x = - \frac{- 1 + 2 c b yr t + 1 - 4 c b yr t + 100 c ^{2} b ^{2} r ^{2} t ^{2}}{2 c b r t}, x = \frac{- 1 + 2 c b yr t - 1 - 4 c b yr t + 100 c ^{2} b ^{2} r ^{2} t ^{2}}{2 c b r t}, x = - \frac{- 1 + 2 c b yr t - 1 - 4 c b yr t + 100 c ^{2} b ^{2} r ^{2} t ^{2}}{2 c b r t}

Schritte zur Lösung

x^{2} + (y - c b r t (x^{2}))^{2} = 25

Schreibe

x^{2} + (y - c b r t (x^{2}))^{2}

um:

x^{2} + y^{2} - 2 c b x^{2} yr t + c^{2} b^{2} x^{4} r^{2} t^{2}

x^{2} + y^{2} - 2 c b x^{2} yr t + c^{2} b^{2} x^{4} r^{2} t^{2} = 25

Verschiebe

25

auf die linke Seite

x^{2} + y^{2} - 2 c b x^{2} yr t + c^{2} b^{2} x^{4} r^{2} t^{2} - 25 = 0

Schreibe in der Standard Form

a_{n} x^{n} + \dots + b x + c = 0

c^{2} b^{2} r^{2} t^{2} x^{4} + (1 - 2 c b yr t) x^{2} + y^{2} - 25 = 0

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

c^{2} b^{2} r^{2} t^{2} u^{2} + (1 - 2 c b yr t) u + y^{2} - 25 = 0

Löse

c^{2} b^{2} r^{2} t^{2} u^{2} + (1 - 2 c b yr t) u + y^{2} - 25 = 0 : u = \frac{- 1 + 2 c b yr t + 1 - 4 c b yr t + 100 c ^{2} b ^{2} r ^{2} t ^{2}}{2 c ^{2} b ^{2} r ^{2} t ^{2}}, u = \frac{- 1 + 2 c b yr t - 1 - 4 c b yr t + 100 c ^{2} b ^{2} r ^{2} t ^{2}}{2 c ^{2} b ^{2} r ^{2} t ^{2}}; c^{2} b^{2} r^{2} t^{2} \neq = 0

u = \frac{- 1 + 2 c b yr t + 1 - 4 c b yr t + 100 c ^{2} b ^{2} r ^{2} t ^{2}}{2 c ^{2} b ^{2} r ^{2} t ^{2}}, u = \frac{- 1 + 2 c b yr t - 1 - 4 c b yr t + 100 c ^{2} b ^{2} r ^{2} t ^{2}}{2 c ^{2} b ^{2} r ^{2} t ^{2}}; c^{2} b^{2} r^{2} t^{2} \neq = 0

Setze

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

löse für

x

Löse

x^{2} = \frac{- 1 + 2 c b yr t + 1 - 4 c b yr t + 100 c ^{2} b ^{2} r ^{2} t ^{2}}{2 c ^{2} b ^{2} r ^{2} t ^{2}} : x = \frac{- 1 + 2 c b yr t + 1 - 4 c b yr t + 100 c ^{2} b ^{2} r ^{2} t ^{2}}{2 c b r t}, x = - \frac{- 1 + 2 c b yr t + 1 - 4 c b yr t + 100 c ^{2} b ^{2} r ^{2} t ^{2}}{2 c b r t}

Löse

x^{2} = \frac{- 1 + 2 c b yr t - 1 - 4 c b yr t + 100 c ^{2} b ^{2} r ^{2} t ^{2}}{2 c ^{2} b ^{2} r ^{2} t ^{2}} : x = \frac{- 1 + 2 c b yr t - 1 - 4 c b yr t + 100 c ^{2} b ^{2} r ^{2} t ^{2}}{2 c b r t}, x = - \frac{- 1 + 2 c b yr t - 1 - 4 c b yr t + 100 c ^{2} b ^{2} r ^{2} t ^{2}}{2 c b r t}

Die Lösungen sind

x = \frac{- 1 + 2 c b yr t + 1 - 4 c b yr t + 100 c ^{2} b ^{2} r ^{2} t ^{2}}{2 c b r t}, x = - \frac{- 1 + 2 c b yr t + 1 - 4 c b yr t + 100 c ^{2} b ^{2} r ^{2} t ^{2}}{2 c b r t}, x = \frac{- 1 + 2 c b yr t - 1 - 4 c b yr t + 100 c ^{2} b ^{2} r ^{2} t ^{2}}{2 c b r t}, x = - \frac{- 1 + 2 c b yr t - 1 - 4 c b yr t + 100 c ^{2} b ^{2} r ^{2} t ^{2}}{2 c b r t}

Graph

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