solvefor a,130r^2-a^2r^3+a^2=0

Lösung

löse nach

a, 130 r^{2} - a^{2} r^{3} + a^{2} = 0

a = i \frac{130 r 1 - r ^{3}}{1 - r ^{3}}, a = - i \frac{130 r 1 - r ^{3}}{1 - r ^{3}}; r \neq = 1, r \neq = - \frac{1}{2} + \frac{3}{2} i, r \neq = - \frac{1}{2} - \frac{3}{2} i

Schritte zur Lösung

130 r^{2} - a^{2} r^{3} + a^{2} = 0

Verschiebe

130 r^{2}

auf die rechte Seite

- a^{2} r^{3} + a^{2} = - 130 r^{2}

Faktorisiere

- a^{2} r^{3} + a^{2} : a^{2} (- r^{3} + 1)

a^{2} (- r^{3} + 1) = - 130 r^{2}

Teile beide Seiten durch

- r^{3} + 1; r \neq = 1, r \neq = - \frac{1}{2} + \frac{3}{2} i, r \neq = - \frac{1}{2} - \frac{3}{2} i

a^{2} = - \frac{130 r ^{2}}{- r ^{3} + 1}; r \neq = 1, r \neq = - \frac{1}{2} + \frac{3}{2} i, r \neq = - \frac{1}{2} - \frac{3}{2} i

Für

x^{2} = f (a)

sind die Lösungen

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

a = - \frac{130 r ^{2}}{- r ^{3} + 1}, a = - - \frac{130 r ^{2}}{- r ^{3} + 1}; r \neq = 1, r \neq = - \frac{1}{2} + \frac{3}{2} i, r \neq = - \frac{1}{2} - \frac{3}{2} i

Vereinfache

- \frac{130 r ^{2}}{- r ^{3} + 1} : i \frac{130 r 1 - r ^{3}}{1 - r ^{3}}

Vereinfache

- - \frac{130 r ^{2}}{- r ^{3} + 1} : - i \frac{130 r 1 - r ^{3}}{1 - r ^{3}}

a = i \frac{130 r 1 - r ^{3}}{1 - r ^{3}}, a = - i \frac{130 r 1 - r ^{3}}{1 - r ^{3}}; r \neq = 1, r \neq = - \frac{1}{2} + \frac{3}{2} i, r \neq = - \frac{1}{2} - \frac{3}{2} i

(3) x = (x^{2} = 9 - 3 = 5)

(2 x - 3)^{2} - (x + 5)^{2} = 0

0.5 x^{2} - 3 x = - x + 2.5

e = x^{2} - 3 x + 5

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