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Beliebt Algebra >

(x^2+ax+2)(x+3)=(x+b)(x^2+cx+6)

Lösung

(x^{2} + a x + 2) (x + 3) = (x + b) (x^{2} + c x + 6)

Lösung

x = \frac{- 3 a + b c + 4 + b ^{2} c ^{2} - 24 b ^{2} + 24 ab + 96 b - 6 ab c - 16 b c + 9 a ^{2} + 24 c - 48 a - 56}{2 ( a - b - c + 3 )}, x = \frac{- 3 a + b c + 4 - b ^{2} c ^{2} - 24 b ^{2} + 24 ab + 96 b - 6 ab c - 16 b c + 9 a ^{2} + 24 c - 48 a - 56}{2 ( a - b - c + 3 )}; a - b - c + 3 \neq = 0

Schritte zur Lösung

(x^{2} + a x + 2) (x + 3) = (x + b) (x^{2} + c x + 6)

Schreibe

(x^{2} + a x + 2) (x + 3)

um:

x^{3} + 3 x^{2} + a x^{2} + 3 a x + 2 x + 6

Schreibe

(x + b) (x^{2} + c x + 6)

um:

x^{3} + c x^{2} + 6 x + b x^{2} + b c x + 6 b

x^{3} + 3 x^{2} + a x^{2} + 3 a x + 2 x + 6 = x^{3} + c x^{2} + 6 x + b x^{2} + b c x + 6 b

Subtrahiere

x^{3} + c x^{2} + 6 x + b x^{2} + b c x + 6 b

von beiden Seiten

x^{3} + 3 x^{2} + a x^{2} + 3 a x + 2 x + 6 - (x^{3} + c x^{2} + 6 x + b x^{2} + b c x + 6 b) = x^{3} + c x^{2} + 6 x + b x^{2} + b c x + 6 b - (x^{3} + c x^{2} + 6 x + b x^{2} + b c x + 6 b)

Vereinfache

(a - b - c + 3) x^{2} + (3 a - b c - 4) x - 6 b + 6 = 0

Löse mit der quadratischen Formel

x_{1, 2} = \frac{- ( 3 a - b c - 4 ) \pm ( 3 a - b c - 4 ) ^{2} - 4 ( a - b - c + 3 ) ( - 6 b + 6 )}{2 ( a - b - c + 3 )}

Vereinfache

(3 a - b c - 4)^{2} - 4 (a - b - c + 3) (- 6 b + 6) : b^{2} c^{2} - 24 b^{2} + 24 ab + 96 b - 6 ab c - 16 b c + 9 a^{2} + 24 c - 48 a - 56

x_{1, 2} = \frac{- ( 3 a - b c - 4 ) \pm b ^{2} c ^{2} - 24 b ^{2} + 24 ab + 96 b - 6 ab c - 16 b c + 9 a ^{2} + 24 c - 48 a - 56}{2 ( a - b - c + 3 )}; a - b - c + 3 \neq = 0

Trenne die Lösungen

x_{1} = \frac{- ( 3 a - b c - 4 ) + b ^{2} c ^{2} - 24 b ^{2} + 24 ab + 96 b - 6 ab c - 16 b c + 9 a ^{2} + 24 c - 48 a - 56}{2 ( a - b - c + 3 )}, x_{2} = \frac{- ( 3 a - b c - 4 ) - b ^{2} c ^{2} - 24 b ^{2} + 24 ab + 96 b - 6 ab c - 16 b c + 9 a ^{2} + 24 c - 48 a - 56}{2 ( a - b - c + 3 )}

x = \frac{- ( 3 a - b c - 4 ) + b ^{2} c ^{2} - 24 b ^{2} + 24 ab + 96 b - 6 ab c - 16 b c + 9 a ^{2} + 24 c - 48 a - 56}{2 ( a - b - c + 3 )} : \frac{- 3 a + b c + 4 + b ^{2} c ^{2} - 24 b ^{2} + 24 ab + 96 b - 6 ab c - 16 b c + 9 a ^{2} + 24 c - 48 a - 56}{2 ( a - b - c + 3 )}

x = \frac{- ( 3 a - b c - 4 ) - b ^{2} c ^{2} - 24 b ^{2} + 24 ab + 96 b - 6 ab c - 16 b c + 9 a ^{2} + 24 c - 48 a - 56}{2 ( a - b - c + 3 )} : \frac{- 3 a + b c + 4 - b ^{2} c ^{2} - 24 b ^{2} + 24 ab + 96 b - 6 ab c - 16 b c + 9 a ^{2} + 24 c - 48 a - 56}{2 ( a - b - c + 3 )}

Die Lösungen für die quadratische Gleichung sind:

x = \frac{- 3 a + b c + 4 + b ^{2} c ^{2} - 24 b ^{2} + 24 ab + 96 b - 6 ab c - 16 b c + 9 a ^{2} + 24 c - 48 a - 56}{2 ( a - b - c + 3 )}, x = \frac{- 3 a + b c + 4 - b ^{2} c ^{2} - 24 b ^{2} + 24 ab + 96 b - 6 ab c - 16 b c + 9 a ^{2} + 24 c - 48 a - 56}{2 ( a - b - c + 3 )}; a - b - c + 3 \neq = 0

Graph

Beliebte Beispiele

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