(e^2sqrt(l)n(x)(1-sqrt(l)n(x))-1)=0

Lösung

(e^{2} l n (x) (1 - l n (x)) - 1) = 0

x = - \frac{- e l + ( e ^{2} - 4 ) l}{2 e l n}, x = \frac{e l + ( e ^{2} - 4 ) l}{2 e l n}; n \neq = 0

Schritte zur Lösung

(e^{2} l n (x) (1 - l n (x)) - 1) = 0

Schreibe

e^{2} l n (x) (1 - l n (x)) - 1

um:

e^{2} n l x - e^{2} l n^{2} x^{2} - 1

e^{2} n l x - e^{2} l n^{2} x^{2} - 1 = 0

Schreibe in der Standard Form

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

- e^{2} l n^{2} x^{2} + e^{2} n l x - 1 = 0

Löse mit der quadratischen Formel

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

Vereinfache

(e^{2} n l)^{2} - 4 (- e^{2} l n^{2}) (- 1) : e n (e^{2} - 4) l

x_{1, 2} = \frac{- e ^{2} n l \pm e n ( e ^{2} - 4 ) l}{2 ( - e ^{2} l n ^{2} )}; n \neq = 0

Trenne die Lösungen

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

x = \frac{- e ^{2} n l + e n ( e ^{2} - 4 ) l}{2 ( - e ^{2} l n ^{2} )} : - \frac{- e l + ( e ^{2} - 4 ) l}{2 e l n}

x = \frac{- e ^{2} n l - e n ( e ^{2} - 4 ) l}{2 ( - e ^{2} l n ^{2} )} : \frac{e l + ( e ^{2} - 4 ) l}{2 e l n}

Die Lösungen für die quadratische Gleichung sind:

x = - \frac{- e l + ( e ^{2} - 4 ) l}{2 e l n}, x = \frac{e l + ( e ^{2} - 4 ) l}{2 e l n}; n \neq = 0

- 4 x^{2} - 2 x + 210 = 0

9 x^{2} - 13 x + 4 = 0

3 x^{2} = 10 x - 8

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

so l v e f or x, 3 x^{2} - 9 y^{2} - 36 z^{2} = 36