x^2+(2-2e^2)x+2=0

Lösung

x^{2} + (2 - 2 e^{2}) x + 2 = 0

x = \frac{- 2 + 2 e ^{2} + 4 e ^{4} - 8 e ^{2} - 4}{2}, x = \frac{- 2 + 2 e ^{2} - 4 e ^{4} - 8 e ^{2} - 4}{2}

Dezimale

x = 12.61962 \dots, x = 0.15848 \dots

Schritte zur Lösung

x^{2} + (2 - 2 e^{2}) x + 2 = 0

Löse mit der quadratischen Formel

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

(2 - 2 e^{2})^{2} - 4 \cdot 1 \cdot 2 = 4 e^{4} - 8 e^{2} - 4

x_{1, 2} = \frac{- ( 2 - 2 e ^{2} ) \pm 4 e ^{4} - 8 e ^{2} - 4}{2 \cdot 1}

Trenne die Lösungen

x_{1} = \frac{- ( 2 - 2 e ^{2} ) + 4 e ^{4} - 8 e ^{2} - 4}{2 \cdot 1}, x_{2} = \frac{- ( 2 - 2 e ^{2} ) - 4 e ^{4} - 8 e ^{2} - 4}{2 \cdot 1}

x = \frac{- ( 2 - 2 e ^{2} ) + 4 e ^{4} - 8 e ^{2} - 4}{2 \cdot 1} : \frac{- 2 + 2 e ^{2} + 4 e ^{4} - 8 e ^{2} - 4}{2}

x = \frac{- ( 2 - 2 e ^{2} ) - 4 e ^{4} - 8 e ^{2} - 4}{2 \cdot 1} : \frac{- 2 + 2 e ^{2} - 4 e ^{4} - 8 e ^{2} - 4}{2}

Die Lösungen für die quadratische Gleichung sind:

x = \frac{- 2 + 2 e ^{2} + 4 e ^{4} - 8 e ^{2} - 4}{2}, x = \frac{- 2 + 2 e ^{2} - 4 e ^{4} - 8 e ^{2} - 4}{2}

so l v e f or v, p = \frac{m v ^{2}}{2}

2 x^{2} - 8 x + 16 = 38

x^{2} - 21 x + 104 = 0

so l v e f or y, x = \frac{1}{2} y^{2} + \frac{1}{4}

x^{2} + 3 x + 3 = - x^{2} + x + 7