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Beliebt Algebra >

solvefor a,8a^2y^2=a^2x^2-x^4

Lösung

löse nach

a, 8 a^{2} y^{2} = a^{2} x^{2} - x^{4}

Lösung

a = i \frac{x ^{2} - x ^{2} + 8 y ^{2}}{- x ^{2} + 8 y ^{2}}, a = - i \frac{x ^{2} - x ^{2} + 8 y ^{2}}{- x ^{2} + 8 y ^{2}}; 8 y^{2} - x^{2} \neq = 0

Schritte zur Lösung

8 a^{2} y^{2} = a^{2} x^{2} - x^{4}

Verschiebe

a^{2} x^{2}

auf die linke Seite

8 a^{2} y^{2} - a^{2} x^{2} = - x^{4}

Faktorisiere

8 a^{2} y^{2} - a^{2} x^{2} : a^{2} (8 y^{2} - x^{2})

a^{2} (8 y^{2} - x^{2}) = - x^{4}

Teile beide Seiten durch

8 y^{2} - x^{2}; 8 y^{2} - x^{2} \neq = 0

a^{2} = - \frac{x ^{4}}{8 y ^{2} - x ^{2}}; 8 y^{2} - x^{2} \neq = 0

Für

x^{2} = f (a)

sind die Lösungen

x = f (a), - f (a)

a = - \frac{x ^{4}}{8 y ^{2} - x ^{2}}, a = - - \frac{x ^{4}}{8 y ^{2} - x ^{2}}; 8 y^{2} - x^{2} \neq = 0

Vereinfache

- \frac{x ^{4}}{8 y ^{2} - x ^{2}} : i \frac{x ^{2} - x ^{2} + 8 y ^{2}}{- x ^{2} + 8 y ^{2}}

Vereinfache

- - \frac{x ^{4}}{8 y ^{2} - x ^{2}} : - i \frac{x ^{2} - x ^{2} + 8 y ^{2}}{- x ^{2} + 8 y ^{2}}

a = i \frac{x ^{2} - x ^{2} + 8 y ^{2}}{- x ^{2} + 8 y ^{2}}, a = - i \frac{x ^{2} - x ^{2} + 8 y ^{2}}{- x ^{2} + 8 y ^{2}}; 8 y^{2} - x^{2} \neq = 0

Graph

Beliebte Beispiele

2 y^{2} = 4 - 7 y

solvefor x,x^2+y^2=1

so l v e f or x, x^{2} + y^{2} = 1

4 x^{2} - 40 x - 12 = 0

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

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