solvefor h,r^2=h^2+(p^2)/(q^2)

Lösung

löse nach

h, r^{2} = h^{2} + \frac{p ^{2}}{q ^{2}}

h = \frac{r ^{2} q ^{2} - p ^{2}}{q}, h = - \frac{r ^{2} q ^{2} - p ^{2}}{q}

Schritte zur Lösung

r^{2} = h^{2} + \frac{p ^{2}}{q ^{2}}

Tausche die Seiten

h^{2} + \frac{p ^{2}}{q ^{2}} = r^{2}

Verschiebe

\frac{p ^{2}}{q ^{2}}

auf die rechte Seite

h^{2} = r^{2} - \frac{p ^{2}}{q ^{2}}

Für

x^{2} = f (a)

sind die Lösungen

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

h = r^{2} - \frac{p ^{2}}{q ^{2}}, h = - r^{2} - \frac{p ^{2}}{q ^{2}}

Vereinfache

r^{2} - \frac{p ^{2}}{q ^{2}} : \frac{r ^{2} q ^{2} - p ^{2}}{q}

Vereinfache

- r^{2} - \frac{p ^{2}}{q ^{2}} : - \frac{r ^{2} q ^{2} - p ^{2}}{q}

h = \frac{r ^{2} q ^{2} - p ^{2}}{q}, h = - \frac{r ^{2} q ^{2} - p ^{2}}{q}

so l v e f or x, f = (m - 3) x^{2} + (4 m - 8) + 3

5 x^{2} + 13 x + 30 = 0, x^{2} + 13 x

so l v e f or x, x^{2} + 2 x y + y^{2} + 3 x + 3 y = 0

so l v e f or m, p^{2} + q^{2} = m^{2}

(\frac{x - 3}{7})^{2} = 4