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Beliebt Algebra >

(a-b)x^2+(b-c)x+(c-a)=0

Lösung

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

Lösung

x = \frac{- b + c + b ^{2} - 4 ab + 2 b c + 4 a ^{2} + c ^{2} - 4 a c}{2 ( a - b )}, x = \frac{- b + c - b ^{2} - 4 ab + 2 b c + 4 a ^{2} + c ^{2} - 4 a c}{2 ( a - b )}; a - b \neq = 0

Schritte zur Lösung

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

Schreibe

(a - b) x^{2} + (b - c) x + (c - a)

um:

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

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

Schreibe in der Standard Form

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

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

Löse mit der quadratischen Formel

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

Vereinfache

(b - c)^{2} - 4 (a - b) (c - a) : b^{2} - 4 ab + 2 b c + 4 a^{2} + c^{2} - 4 a c

x_{1, 2} = \frac{- ( b - c ) \pm b ^{2} - 4 ab + 2 b c + 4 a ^{2} + c ^{2} - 4 a c}{2 ( a - b )}; a - b \neq = 0

Trenne die Lösungen

x_{1} = \frac{- ( b - c ) + b ^{2} - 4 ab + 2 b c + 4 a ^{2} + c ^{2} - 4 a c}{2 ( a - b )}, x_{2} = \frac{- ( b - c ) - b ^{2} - 4 ab + 2 b c + 4 a ^{2} + c ^{2} - 4 a c}{2 ( a - b )}

x = \frac{- ( b - c ) + b ^{2} - 4 ab + 2 b c + 4 a ^{2} + c ^{2} - 4 a c}{2 ( a - b )} : \frac{- b + c + b ^{2} - 4 ab + 2 b c + 4 a ^{2} + c ^{2} - 4 a c}{2 ( a - b )}

x = \frac{- ( b - c ) - b ^{2} - 4 ab + 2 b c + 4 a ^{2} + c ^{2} - 4 a c}{2 ( a - b )} : \frac{- b + c - b ^{2} - 4 ab + 2 b c + 4 a ^{2} + c ^{2} - 4 a c}{2 ( a - b )}

Die Lösungen für die quadratische Gleichung sind:

x = \frac{- b + c + b ^{2} - 4 ab + 2 b c + 4 a ^{2} + c ^{2} - 4 a c}{2 ( a - b )}, x = \frac{- b + c - b ^{2} - 4 ab + 2 b c + 4 a ^{2} + c ^{2} - 4 a c}{2 ( a - b )}; a - b \neq = 0

Graph

Beliebte Beispiele

x^2-2(a^2+b^2)x+(a^2-b^2)=0

x^{2} - 2 (a^{2} + b^{2}) x + (a^{2} - b^{2}) = 0

solvefor x,p^3-(x^2+xy+y^2)*p+xy(x+y)=0

so l v e f or x, p^{3} - (x^{2} + x y + y^{2}) \cdot p + x y (x + y) = 0

5/2*x+2/3*x= 95/2*x^2

\frac{5}{2} \cdot x + \frac{2}{3} \cdot x = \frac{95}{2} \cdot x^{2}

solvefor x,4x^2-4xy+y^2-4x-8y-20=0

so l v e f or x, 4 x^{2} - 4 x y + y^{2} - 4 x - 8 y - 20 = 0

v^{1} c^{1} = v^{2} c^{2}