de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Algebra >

solvefor z,z^2(p^2z^2+q^2)=1

Lösung

löse nach

z, z^{2} (p^{2} z^{2} + q^{2}) = 1

Lösung

z = \frac{- q ^{2} + q ^{4} + 4 p ^{2}}{2 p}, z = - \frac{- q ^{2} + q ^{4} + 4 p ^{2}}{2 p}, z = \frac{- q ^{2} - q ^{4} + 4 p ^{2}}{2 p}, z = - \frac{- q ^{2} - q ^{4} + 4 p ^{2}}{2 p}

Schritte zur Lösung

z^{2} (p^{2} z^{2} + q^{2}) = 1

Schreibe

z^{2} (p^{2} z^{2} + q^{2})

um:

z^{4} p^{2} + z^{2} q^{2}

z^{4} p^{2} + z^{2} q^{2} = 1

Verschiebe

1

auf die linke Seite

z^{4} p^{2} + z^{2} q^{2} - 1 = 0

Schreibe in der Standard Form

a_{n} x^{n} + \dots + q x + p = 0

p^{2} z^{4} + q^{2} z^{2} - 1 = 0

Schreibe die Gleichung um mit

u = z^{2}

und

u^{2} = z^{4}

p^{2} u^{2} + q^{2} u - 1 = 0

Löse

p^{2} u^{2} + q^{2} u - 1 = 0 : u = \frac{- q ^{2} + q ^{4} + 4 p ^{2}}{2 p ^{2}}, u = \frac{- q ^{2} - q ^{4} + 4 p ^{2}}{2 p ^{2}}; p \neq = 0

u = \frac{- q ^{2} + q ^{4} + 4 p ^{2}}{2 p ^{2}}, u = \frac{- q ^{2} - q ^{4} + 4 p ^{2}}{2 p ^{2}}; p \neq = 0

Setze

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

löse für

z

Löse

z^{2} = \frac{- q ^{2} + q ^{4} + 4 p ^{2}}{2 p ^{2}} : z = \frac{- q ^{2} + q ^{4} + 4 p ^{2}}{2 p}, z = - \frac{- q ^{2} + q ^{4} + 4 p ^{2}}{2 p}

Löse

z^{2} = \frac{- q ^{2} - q ^{4} + 4 p ^{2}}{2 p ^{2}} : z = \frac{- q ^{2} - q ^{4} + 4 p ^{2}}{2 p}, z = - \frac{- q ^{2} - q ^{4} + 4 p ^{2}}{2 p}

Die Lösungen sind

z = \frac{- q ^{2} + q ^{4} + 4 p ^{2}}{2 p}, z = - \frac{- q ^{2} + q ^{4} + 4 p ^{2}}{2 p}, z = \frac{- q ^{2} - q ^{4} + 4 p ^{2}}{2 p}, z = - \frac{- q ^{2} - q ^{4} + 4 p ^{2}}{2 p}

Graph

Beliebte Beispiele

(x^2-6)(x^2-1)=0

(x^{2} - 6) (x^{2} - 1) = 0

2 x^{4} - 81 = 0

(x^2-2)^2-10(x^2-2)+21=0

(x^{2} - 2)^{2} - 10 (x^{2} - 2) + 21 = 0

9x^2-24x^{16}=0

9 x^{2} - 24 x^{16} = 0

x^{3} - 5 x^{2} = 0