solvefor b,a(a+b)(a+b+c)=11

Lösung

löse nach

b, a (a + b) (a + b + c) = 11

b = \frac{- 2 a ^{2} - a c + a ^{2} c ^{2} + 44 a}{2 a}, b = \frac{- 2 a ^{2} - a c - a ^{2} c ^{2} + 44 a}{2 a}; a \neq = 0

Schritte zur Lösung

a (a + b) (a + b + c) = 11

Schreibe

a (a + b) (a + b + c)

um:

2 b a^{2} + a^{2} c + a^{3} + b^{2} a + ba c

2 b a^{2} + a^{2} c + a^{3} + b^{2} a + ba c = 11

Verschiebe

11

auf die linke Seite

2 b a^{2} + a^{2} c + a^{3} + b^{2} a + ba c - 11 = 0

Schreibe in der Standard Form

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

a b^{2} + (2 a^{2} + a c) b + a^{2} c + a^{3} - 11 = 0

Löse mit der quadratischen Formel

b_{1, 2} = \frac{- ( 2 a ^{2} + a c ) \pm ( 2 a ^{2} + a c ) ^{2} - 4 a ( a ^{2} c + a ^{3} - 11 )}{2 a}

Vereinfache

(2 a^{2} + a c)^{2} - 4 a (a^{2} c + a^{3} - 11) : a^{2} c^{2} + 44 a

b_{1, 2} = \frac{- ( 2 a ^{2} + a c ) \pm a ^{2} c ^{2} + 44 a}{2 a}; a \neq = 0

Trenne die Lösungen

b_{1} = \frac{- ( 2 a ^{2} + a c ) + a ^{2} c ^{2} + 44 a}{2 a}, b_{2} = \frac{- ( 2 a ^{2} + a c ) - a ^{2} c ^{2} + 44 a}{2 a}

b = \frac{- ( 2 a ^{2} + a c ) + a ^{2} c ^{2} + 44 a}{2 a} : \frac{- 2 a ^{2} - a c + a ^{2} c ^{2} + 44 a}{2 a}

b = \frac{- ( 2 a ^{2} + a c ) - a ^{2} c ^{2} + 44 a}{2 a} : \frac{- 2 a ^{2} - a c - a ^{2} c ^{2} + 44 a}{2 a}

Die Lösungen für die quadratische Gleichung sind:

b = \frac{- 2 a ^{2} - a c + a ^{2} c ^{2} + 44 a}{2 a}, b = \frac{- 2 a ^{2} - a c - a ^{2} c ^{2} + 44 a}{2 a}; a \neq = 0

2 d^{2} + 5 d - 12 = 0

z^{2} - 12 z + 36 = - 64

3 (x + 7)^{2} = 7

(x) = 3 x^{2} - 48 x + 350

(x - 6)^{2} + 10 (x - 6) = 0