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Beliebt Algebra >

2x^2-6x+6=c^1(x^2+x-1)+c^2(x^2-x+1)

Lösung

2 x^{2} - 6 x + 6 = c^{1} (x^{2} + x - 1) + c^{2} (x^{2} - x + 1)

Lösung

x = \frac{6 - c ^{2} + c + c - ( 3 c - 1 ) ( c - 3 ) + 2 - ( 3 c - 1 ) ( c - 3 )}{2 ( 2 - c ^{2} - c )}, x = \frac{6 - c ^{2} + c - c - ( 3 c - 1 ) ( c - 3 ) - 2 - ( 3 c - 1 ) ( c - 3 )}{2 ( 2 - c ^{2} - c )}; c \neq = - 2, c \neq = 1

Schritte zur Lösung

2 x^{2} - 6 x + 6 = c^{1} (x^{2} + x - 1) + c^{2} (x^{2} - x + 1)

Schreibe

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

um:

c x^{2} + c x - c + c^{2} x^{2} - c^{2} x + c^{2}

2 x^{2} - 6 x + 6 = c x^{2} + c x - c + c^{2} x^{2} - c^{2} x + c^{2}

Subtrahiere

c^{2} x^{2} - c^{2} x + c^{2}

von beiden Seiten

2 x^{2} - 6 x + 6 - (c^{2} x^{2} - c^{2} x + c^{2}) = c x^{2} + c x - c + c^{2} x^{2} - c^{2} x + c^{2} - (c^{2} x^{2} - c^{2} x + c^{2})

Vereinfache

2 x^{2} - 6 x + 6 - c^{2} x^{2} + c^{2} x - c^{2} = c x^{2} + c x - c

Subtrahiere

c x - c

von beiden Seiten

2 x^{2} - 6 x + 6 - c^{2} x^{2} + c^{2} x - c^{2} - (c x - c) = c x^{2} + c x - c - (c x - c)

Vereinfache

2 x^{2} - 6 x + 6 - c^{2} x^{2} + c^{2} x - c^{2} - c x + c = c x^{2}

Verschiebe

c x^{2}

auf die linke Seite

2 x^{2} - 6 x + 6 - c^{2} x^{2} + c^{2} x - c^{2} - c x + c - c x^{2} = 0

Schreibe in der Standard Form

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

(2 - c^{2} - c) x^{2} + (- 6 + c^{2} - c) x + 6 - c^{2} + c = 0

Löse mit der quadratischen Formel

x_{1, 2} = \frac{- ( - 6 + c ^{2} - c ) \pm ( - 6 + c ^{2} - c ) ^{2} - 4 ( 2 - c ^{2} - c ) ( 6 - c ^{2} + c )}{2 ( 2 - c ^{2} - c )}

Vereinfache

(- 6 + c^{2} - c)^{2} - 4 (2 - c^{2} - c) (6 - c^{2} + c) : (c + 2) - (3 c - 1) (c - 3)

x_{1, 2} = \frac{- ( - 6 + c ^{2} - c ) \pm ( c + 2 ) - ( 3 c - 1 ) ( c - 3 )}{2 ( 2 - c ^{2} - c )}; c \neq = - 2, c \neq = 1

Trenne die Lösungen

x_{1} = \frac{- ( - 6 + c ^{2} - c ) + ( c + 2 ) - ( 3 c - 1 ) ( c - 3 )}{2 ( 2 - c ^{2} - c )}, x_{2} = \frac{- ( - 6 + c ^{2} - c ) - ( c + 2 ) - ( 3 c - 1 ) ( c - 3 )}{2 ( 2 - c ^{2} - c )}

x = \frac{- ( - 6 + c ^{2} - c ) + ( c + 2 ) - ( 3 c - 1 ) ( c - 3 )}{2 ( 2 - c ^{2} - c )} : \frac{6 - c ^{2} + c + c - ( 3 c - 1 ) ( c - 3 ) + 2 - ( 3 c - 1 ) ( c - 3 )}{2 ( 2 - c ^{2} - c )}

x = \frac{- ( - 6 + c ^{2} - c ) - ( c + 2 ) - ( 3 c - 1 ) ( c - 3 )}{2 ( 2 - c ^{2} - c )} : \frac{6 - c ^{2} + c - c - ( 3 c - 1 ) ( c - 3 ) - 2 - ( 3 c - 1 ) ( c - 3 )}{2 ( 2 - c ^{2} - c )}

Die Lösungen für die quadratische Gleichung sind:

x = \frac{6 - c ^{2} + c + c - ( 3 c - 1 ) ( c - 3 ) + 2 - ( 3 c - 1 ) ( c - 3 )}{2 ( 2 - c ^{2} - c )}, x = \frac{6 - c ^{2} + c - c - ( 3 c - 1 ) ( c - 3 ) - 2 - ( 3 c - 1 ) ( c - 3 )}{2 ( 2 - c ^{2} - c )}; c \neq = - 2, c \neq = 1

Graph

Beliebte Beispiele

(2x-10)(3x+12)=0

(2 x - 10) (3 x + 12) = 0

a^{2} - 2 a = 2

completesquare x^2+4x-16

co m pl e t es q u a re x^{2} + 4 x - 16

x^{2} + 2 x - 40 = 0

a= a/(360)pir^2

a = \frac{a}{360} π r^{2}