solvefor x,x^2-x+1-2k(x)^2+4k+1=0

Lösung

löse nach

x, x^{2} - x + 1 - 2 k (x)^{2} + 4 k + 1 = 0

x = \frac{1 + 32 k ^{2} - 7}{2 ( 1 - 2 k )}, x = \frac{1 - 32 k ^{2} - 7}{2 ( 1 - 2 k )}; k \neq = \frac{1}{2}

Schritte zur Lösung

x^{2} - x + 1 - 2 k x^{2} + 4 k + 1 = 0

Schreibe

x^{2} - x + 1 - 2 k x^{2} + 4 k + 1

um:

x^{2} - 2 x^{2} k - x + 4 k + 2

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

Schreibe in der Standard Form

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

(1 - 2 k) x^{2} - x + 4 k + 2 = 0

Löse mit der quadratischen Formel

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

Vereinfache

(- 1)^{2} - 4 (1 - 2 k) (4 k + 2) : 32 k^{2} - 7

x_{1, 2} = \frac{- ( - 1 ) \pm 32 k ^{2} - 7}{2 ( 1 - 2 k )}; k \neq = \frac{1}{2}

Trenne die Lösungen

x_{1} = \frac{- ( - 1 ) + 32 k ^{2} - 7}{2 ( 1 - 2 k )}, x_{2} = \frac{- ( - 1 ) - 32 k ^{2} - 7}{2 ( 1 - 2 k )}

x = \frac{- ( - 1 ) + 32 k ^{2} - 7}{2 ( 1 - 2 k )} : \frac{1 + 32 k ^{2} - 7}{2 ( 1 - 2 k )}

x = \frac{- ( - 1 ) - 32 k ^{2} - 7}{2 ( 1 - 2 k )} : \frac{1 - 32 k ^{2} - 7}{2 ( 1 - 2 k )}

Die Lösungen für die quadratische Gleichung sind:

x = \frac{1 + 32 k ^{2} - 7}{2 ( 1 - 2 k )}, x = \frac{1 - 32 k ^{2} - 7}{2 ( 1 - 2 k )}; k \neq = \frac{1}{2}

((\frac{( x - 5 ) ( x - 5 )}{y ^{2}})) = \frac{1}{y ^{2}} + 1

- 2 x^{2} + 4 y^{2} - 3 x - 43 y + 44 = 0

9 x^{2} - 36 x - 25 y^{2} = - 261

3 x^{2} - 6 x - y^{2} - 4 y - 4 = 0

4 y^{2} - 4 x^{2} + 1^{2} = 4