solvefor a,(x^2+y^2+z^2)=a^2z^4

Lösung

löse nach

a, (x^{2} + y^{2} + z^{2}) = a^{2} z^{4}

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

Schritte zur Lösung

(x^{2} + y^{2} + z^{2}) = a^{2} z^{4}

Tausche die Seiten

a^{2} z^{4} = (x^{2} + y^{2} + z^{2})

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

Teile beide Seiten durch

z^{4}; z \neq = 0

a^{2} = \frac{x ^{2} + y ^{2} + z ^{2}}{z ^{4}}; z \neq = 0

Für

x^{2} = f (a)

sind die Lösungen

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

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

Vereinfache

\frac{x ^{2} + y ^{2} + z ^{2}}{z ^{4}} : \frac{x ^{2} + y ^{2} + z ^{2}}{z ^{2}}

Vereinfache

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

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

x^{2} + x - 7 = - 2 x

f a c t or 2 x^{2} - 3 x = 0

x^{2} + 16 x - 48 = 0

2 x^{2} - x + 55 = 0

x^{2} - 16 x + 5 = 0