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

Lösung

löse nach

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

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

Schritte zur Lösung

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

Tausche die Seiten

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

Teile beide Seiten durch

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

a^{2} = \frac{( x ^{2} + y ^{2} ) ^{2}}{x ^{2} - y ^{2}}; x^{2} - y^{2} \neq = 0

Für

x^{2} = f (a)

sind die Lösungen

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

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

Vereinfache

\frac{( x ^{2} + y ^{2} ) ^{2}}{x ^{2} - y ^{2}} : \frac{x ^{2} + y ^{2}}{x ^{2} - y ^{2}}

Vereinfache

- \frac{( x ^{2} + y ^{2} ) ^{2}}{x ^{2} - y ^{2}} : - \frac{x ^{2} + y ^{2}}{x ^{2} - y ^{2}}

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

(n + 4) + n (n + 2) + n = 0

4 r^{2} = 25

(130 π \cdot 1 0^{3} - w)^{2} = 3 \cdot 150 π \cdot 1 0^{3}

4 x^{2} + 7 = 0

4 x + 12 x^{2} = 0