(m-1)*x^2-2(m-1)x+1=0

Lösung

(m - 1) \cdot x^{2} - 2 (m - 1) x + 1 = 0

x = \frac{m - 1 + m ^{2} - 3 m + 2}{m - 1}, x = \frac{m - 1 - m ^{2} - 3 m + 2}{m - 1}; m \neq = 1

Schritte zur Lösung

(m - 1) x^{2} - 2 (m - 1) x + 1 = 0

Schreibe

(m - 1) x^{2} - 2 (m - 1) x + 1

um:

m x^{2} - x^{2} - 2 m x + 2 x + 1

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

Schreibe in der Standard Form

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

(m - 1) x^{2} + (- 2 m + 2) x + 1 = 0

Löse mit der quadratischen Formel

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

Vereinfache

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

x_{1, 2} = \frac{- ( - 2 m + 2 ) \pm 2 m ^{2} - 3 m + 2}{2 ( m - 1 )}; m \neq = 1

Trenne die Lösungen

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

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

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

Die Lösungen für die quadratische Gleichung sind:

x = \frac{m - 1 + m ^{2} - 3 m + 2}{m - 1}, x = \frac{m - 1 - m ^{2} - 3 m + 2}{m - 1}; m \neq = 1

so l v e f or x, y^{2} = \frac{( 9 x ^{2} )}{36}

so l v e f or x, w = x^{2} - 25

x (5 x - 7) = - 2

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

(\frac{2 x + 3}{4})^{2} = \frac{49}{25}