de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Algebra >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Verschiebe

a^{2}

auf die rechte Seite

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

Faktorisiere

130 r^{3} - a^{2} r^{3} : r^{3} (130 - a^{2})

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

Teile beide Seiten durch

130 - a^{2}; a \neq = 130, a \neq = - 130

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

Für

x^{3} = f (a)

sind die Lösungen

x = 3 f (a), 3 f (a) \frac{- 1 - 3 i}{2}, 3 f (a) \frac{- 1 + 3 i}{2}

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

Vereinfache

3 - \frac{a ^{2}}{130 - a ^{2}} : - 3 \frac{a ^{2}}{130 - a ^{2}}

Vereinfache

3 - \frac{a ^{2}}{130 - a ^{2}} \frac{- 1 + 3 i}{2} : - \frac{3 a ^{2} ( - 1 + 3 i )}{2 3 130 - a ^{2}}

Vereinfache

3 - \frac{a ^{2}}{130 - a ^{2}} \frac{- 1 - 3 i}{2} : - \frac{3 a ^{2} ( - 1 - 3 i )}{2 3 130 - a ^{2}}

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

Graph

Beliebte Beispiele

x^{5} = 212

2 x^{3} + 2 x + x = - 1

3 + 9 x^{5} - 20 = 40

2 y^{3} - 5 y^{2} = 1

3x^3+5x^2-16x+4=0

3 x^{3} + 5 x^{2} - 16 x + 4 = 0