m^2x^2+2mx+1-n^2=0

Lösung

m^{2} x^{2} + 2 m x + 1 - n^{2} = 0

x = \frac{- 1 + n}{m}, x = - \frac{n + 1}{m}; m \neq = 0

Schritte zur Lösung

m^{2} x^{2} + 2 m x + 1 - n^{2} = 0

Löse mit der quadratischen Formel

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

Vereinfache

(2 m)^{2} - 4 m^{2} (1 - n^{2}) : 2 mn

x_{1, 2} = \frac{- 2 m \pm 2 mn}{2 m ^{2}}; m \neq = 0

Trenne die Lösungen

x_{1} = \frac{- 2 m + 2 mn}{2 m ^{2}}, x_{2} = \frac{- 2 m - 2 mn}{2 m ^{2}}

x = \frac{- 2 m + 2 mn}{2 m ^{2}} : \frac{- 1 + n}{m}

x = \frac{- 2 m - 2 mn}{2 m ^{2}} : - \frac{n + 1}{m}

Die Lösungen für die quadratische Gleichung sind:

x = \frac{- 1 + n}{m}, x = - \frac{n + 1}{m}; m \neq = 0

a^{2} + 5^{2} = 1 0^{2}

(x - 5) (x - 1) = 0

x^{2} - 18 x - 10 = 0

x^{2} + 8 + 15 = 0

X^{2} - 5 X + 1 = 0