de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Algebra >

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

Lösung

löse nach

y, (x^{2} + y^{2})^{2} = x^{2} - y^{2}

Lösung

y = \frac{- 2 x ^{2} - 1 + 8 x ^{2} + 1}{2}, y = - \frac{- 2 x ^{2} - 1 + 8 x ^{2} + 1}{2}, y = \frac{- 2 x ^{2} - 1 - 8 x ^{2} + 1}{2}, y = - \frac{- 2 x ^{2} - 1 - 8 x ^{2} + 1}{2}

Schritte zur Lösung

(x^{2} + y^{2})^{2} = x^{2} - y^{2}

Schreibe

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

um:

x^{4} + 2 y^{2} x^{2} + y^{4}

x^{4} + 2 y^{2} x^{2} + y^{4} = x^{2} - y^{2}

Verschiebe

y^{2}

auf die linke Seite

x^{4} + 2 y^{2} x^{2} + y^{4} + y^{2} = x^{2}

Verschiebe

x^{2}

auf die linke Seite

x^{4} + 2 y^{2} x^{2} + y^{4} + y^{2} - x^{2} = 0

Schreibe in der Standard Form

a_{n} x^{n} + \dots + a_{1} x + x = 0

y^{4} + (2 x^{2} + 1) y^{2} + x^{4} - x^{2} = 0

Schreibe die Gleichung um mit

u = y^{2}

und

u^{2} = y^{4}

u^{2} + (2 x^{2} + 1) u + x^{4} - x^{2} = 0

Löse

u^{2} + (2 x^{2} + 1) u + x^{4} - x^{2} = 0 : u = \frac{- 2 x ^{2} - 1 + 8 x ^{2} + 1}{2}, u = \frac{- 2 x ^{2} - 1 - 8 x ^{2} + 1}{2}

u = \frac{- 2 x ^{2} - 1 + 8 x ^{2} + 1}{2}, u = \frac{- 2 x ^{2} - 1 - 8 x ^{2} + 1}{2}

Setze

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

löse für

y

Löse

y^{2} = \frac{- 2 x ^{2} - 1 + 8 x ^{2} + 1}{2} : y = \frac{- 2 x ^{2} - 1 + 8 x ^{2} + 1}{2}, y = - \frac{- 2 x ^{2} - 1 + 8 x ^{2} + 1}{2}

Löse

y^{2} = \frac{- 2 x ^{2} - 1 - 8 x ^{2} + 1}{2} : y = \frac{- 2 x ^{2} - 1 - 8 x ^{2} + 1}{2}, y = - \frac{- 2 x ^{2} - 1 - 8 x ^{2} + 1}{2}

Die Lösungen sind

y = \frac{- 2 x ^{2} - 1 + 8 x ^{2} + 1}{2}, y = - \frac{- 2 x ^{2} - 1 + 8 x ^{2} + 1}{2}, y = \frac{- 2 x ^{2} - 1 - 8 x ^{2} + 1}{2}, y = - \frac{- 2 x ^{2} - 1 - 8 x ^{2} + 1}{2}

Graph

Beliebte Beispiele

wurzeln von x^3-x^2-x+1=0

roo t s x^{3} - x^{2} - x + 1 = 0

3x^5-8x^4+2x^3+5x^2-2x+1=0

3 x^{5} - 8 x^{4} + 2 x^{3} + 5 x^{2} - 2 x + 1 = 0

2 x^{3} - 6 x + 4 = 0

x^4+9x^3+23x^2+3x-36=0

x^{4} + 9 x^{3} + 23 x^{2} + 3 x - 36 = 0

6x^5+11x^4-39x^3-41x^2+45x+18=0

6 x^{5} + 11 x^{4} - 39 x^{3} - 41 x^{2} + 45 x + 18 = 0