(a+b)2x^2+6(a^2-b^2)x+9(a-b)2=0

Lösung

(a + b) 2 x^{2} + 6 (a^{2} - b^{2}) x + 9 (a - b) 2 = 0

x = \frac{- 6 a ^{2} + 6 b ^{2} + ( 6 a ^{2} - 6 b ^{2} ) ^{2} - 4 ( 2 a + 2 b ) ( 18 a - 18 b )}{2 ( 2 a + 2 b )}, x = \frac{- 6 a ^{2} + 6 b ^{2} - ( 6 a ^{2} - 6 b ^{2} ) ^{2} - 4 ( 2 a + 2 b ) ( 18 a - 18 b )}{2 ( 2 a + 2 b )}; 2 a + 2 b \neq = 0

Schritte zur Lösung

(a + b) \cdot 2 x^{2} + 6 (a^{2} - b^{2}) x + 9 (a - b) \cdot 2 = 0

Schreibe

(a + b) \cdot 2 x^{2} + 6 (a^{2} - b^{2}) x + 9 (a - b) \cdot 2

um:

2 a x^{2} + 2 b x^{2} + 6 a^{2} x - 6 b^{2} x + 18 a - 18 b

2 a x^{2} + 2 b x^{2} + 6 a^{2} x - 6 b^{2} x + 18 a - 18 b = 0

Schreibe in der Standard Form

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

(2 a + 2 b) x^{2} + (6 a^{2} - 6 b^{2}) x + 18 a - 18 b = 0

Löse mit der quadratischen Formel

x_{1, 2} = \frac{- ( 6 a ^{2} - 6 b ^{2} ) \pm ( 6 a ^{2} - 6 b ^{2} ) ^{2} - 4 ( 2 a + 2 b ) ( 18 a - 18 b )}{2 ( 2 a + 2 b )}

x = \frac{- ( 6 a ^{2} - 6 b ^{2} ) + ( 6 a ^{2} - 6 b ^{2} ) ^{2} - 4 ( 2 a + 2 b ) ( 18 a - 18 b )}{2 ( 2 a + 2 b )} : \frac{- 6 a ^{2} + 6 b ^{2} + ( 6 a ^{2} - 6 b ^{2} ) ^{2} - 4 ( 2 a + 2 b ) ( 18 a - 18 b )}{2 ( 2 a + 2 b )}

x = \frac{- ( 6 a ^{2} - 6 b ^{2} ) - ( 6 a ^{2} - 6 b ^{2} ) ^{2} - 4 ( 2 a + 2 b ) ( 18 a - 18 b )}{2 ( 2 a + 2 b )} : \frac{- 6 a ^{2} + 6 b ^{2} - ( 6 a ^{2} - 6 b ^{2} ) ^{2} - 4 ( 2 a + 2 b ) ( 18 a - 18 b )}{2 ( 2 a + 2 b )}

Die Lösungen für die quadratische Gleichung sind:

x = \frac{- 6 a ^{2} + 6 b ^{2} + ( 6 a ^{2} - 6 b ^{2} ) ^{2} - 4 ( 2 a + 2 b ) ( 18 a - 18 b )}{2 ( 2 a + 2 b )}, x = \frac{- 6 a ^{2} + 6 b ^{2} - ( 6 a ^{2} - 6 b ^{2} ) ^{2} - 4 ( 2 a + 2 b ) ( 18 a - 18 b )}{2 ( 2 a + 2 b )}; 2 a + 2 b \neq = 0

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

so l v e f or a, 130 r^{2} - a^{2} r^{3} + a^{2} = 0

(3) x = (x^{2} = 9 - 3 = 5)

(2 x - 3)^{2} - (x + 5)^{2} = 0

0.5 x^{2} - 3 x = - x + 2.5