x^2+((a+1)/a)x+1=0

Lösung

x^{2} + (\frac{a + 1}{a}) x + 1 = 0

x = \frac{- a - 1 + 2 a + 1 - 3 a ^{2}}{2 a}, x = \frac{- a - 1 - 2 a + 1 - 3 a ^{2}}{2 a}

Schritte zur Lösung

x^{2} + (\frac{a + 1}{a}) x + 1 = 0

Schreibe

x^{2} + (\frac{a + 1}{a}) x + 1

um:

x^{2} + x + \frac{x}{a} + 1

x^{2} + x + \frac{x}{a} + 1 = 0

Schreibe in der Standard Form

a x^{2} + b x + c = 0

x^{2} + (1 + \frac{1}{a}) x + 1 = 0

Löse mit der quadratischen Formel

x_{1, 2} = \frac{- ( 1 + \frac{1}{a} ) \pm ( 1 + \frac{1}{a} ) ^{2} - 4 \cdot 1 \cdot 1}{2 \cdot 1}

Vereinfache

(1 + \frac{1}{a})^{2} - 4 \cdot 1 \cdot 1 : \frac{2 a + 1 - 3 a ^{2}}{a}

x_{1, 2} = \frac{- ( 1 + \frac{1}{a} ) \pm \frac{2 a + 1 - 3 a ^{2}}{a}}{2 \cdot 1}

Trenne die Lösungen

x_{1} = \frac{- ( 1 + \frac{1}{a} ) + \frac{2 a + 1 - 3 a ^{2}}{a}}{2 \cdot 1}, x_{2} = \frac{- ( 1 + \frac{1}{a} ) - \frac{2 a + 1 - 3 a ^{2}}{a}}{2 \cdot 1}

x = \frac{- ( 1 + \frac{1}{a} ) + \frac{2 a + 1 - 3 a ^{2}}{a}}{2 \cdot 1} : \frac{- a - 1 + 2 a + 1 - 3 a ^{2}}{2 a}

x = \frac{- ( 1 + \frac{1}{a} ) - \frac{2 a + 1 - 3 a ^{2}}{a}}{2 \cdot 1} : \frac{- a - 1 - 2 a + 1 - 3 a ^{2}}{2 a}

Die Lösungen für die quadratische Gleichung sind:

x = \frac{- a - 1 + 2 a + 1 - 3 a ^{2}}{2 a}, x = \frac{- a - 1 - 2 a + 1 - 3 a ^{2}}{2 a}

x^{2} + 8 x - 1920 = 0

so l v e f or y, y^{2} = x^{5} (2 a - x)

so l v e f or x, p \cdot x^{2} - (3 p + 2) \cdot x + (5 p - 2) = 0

so l v e f or x, y^{3} - 7 y - 6 y = e^{2} x (1 + x)

so l v e f or b, a = b (b + 2 a)