1/(d^2)=(h^2+k^2)/(a^2)+(l^2)/(c^2)

Lösung

\frac{1}{d ^{2}} = \frac{h ^{2} + k ^{2}}{a ^{2}} + \frac{l ^{2}}{c ^{2}}

h = \frac{- k ^{2} d ^{2} c ^{2} + a ^{2} c ^{2} - a ^{2} l ^{2} d ^{2}}{d c}, h = - \frac{- k ^{2} d ^{2} c ^{2} + a ^{2} c ^{2} - a ^{2} l ^{2} d ^{2}}{d c}; a \neq = 0

Schritte zur Lösung

\frac{1}{d ^{2}} = \frac{h ^{2} + k ^{2}}{a ^{2}} + \frac{l ^{2}}{c ^{2}}

Tausche die Seiten

\frac{h ^{2} + k ^{2}}{a ^{2}} + \frac{l ^{2}}{c ^{2}} = \frac{1}{d ^{2}}

Verschiebe

\frac{l ^{2}}{c ^{2}}

auf die rechte Seite

\frac{h ^{2} + k ^{2}}{a ^{2}} = \frac{1}{d ^{2}} - \frac{l ^{2}}{c ^{2}}

Multipliziere beide Seiten mit

a^{2}

h^{2} + k^{2} = \frac{a ^{2}}{d ^{2}} - \frac{a ^{2} l ^{2}}{c ^{2}}; a \neq = 0

Verschiebe

k^{2}

auf die rechte Seite

h^{2} = \frac{a ^{2}}{d ^{2}} - \frac{a ^{2} l ^{2}}{c ^{2}} - k^{2}; a \neq = 0

Für

x^{2} = f (a)

sind die Lösungen

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

h = \frac{a ^{2}}{d ^{2}} - \frac{a ^{2} l ^{2}}{c ^{2}} - k^{2}, h = - \frac{a ^{2}}{d ^{2}} - \frac{a ^{2} l ^{2}}{c ^{2}} - k^{2}; a \neq = 0

Vereinfache

\frac{a ^{2}}{d ^{2}} - \frac{a ^{2} l ^{2}}{c ^{2}} - k^{2} : \frac{- k ^{2} d ^{2} c ^{2} + a ^{2} c ^{2} - a ^{2} l ^{2} d ^{2}}{d c}

Vereinfache

- \frac{a ^{2}}{d ^{2}} - \frac{a ^{2} l ^{2}}{c ^{2}} - k^{2} : - \frac{- k ^{2} d ^{2} c ^{2} + a ^{2} c ^{2} - a ^{2} l ^{2} d ^{2}}{d c}

h = \frac{- k ^{2} d ^{2} c ^{2} + a ^{2} c ^{2} - a ^{2} l ^{2} d ^{2}}{d c}, h = - \frac{- k ^{2} d ^{2} c ^{2} + a ^{2} c ^{2} - a ^{2} l ^{2} d ^{2}}{d c}; a \neq = 0

so l v e f or x, x^{2} + y^{2} - 4 x - 2 y + 85 = 0

so l v e f or d, d^{2} y - 4 e^{5 x} = 0

3 x^{2} - 30 x + 74 = 0

5 x^{2} + 38 x + 21 = (5 x + 3)

7 = \frac{1}{12} x^{2} + \frac{2}{3} x