2. GLEICHUNGEN, GLEICHUNGSSYSTEME - Mathe Online

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Gleichungen, Gleichungssysteme
Isolieren einer Wurzel: x + 13 = 1 + x + 6
x + 13 = + x + 6 2
(1 ) | ( )²
x + 13 = 1 + 2 x + 6 + x + 6
2 x + 6 = 6
x + 6 = 3 | ( )²
x + 6 = 9
x = 3
Probe: LS : 3+ 13 − 3+ 6 = 16 − 9 = 4 − 3 = 1
RS: 1
L = {3}
Beispiel: x + 5 + x + 12 = 4x + 33 , G = R
Definitionsmenge: D1 = { x x ≥−5 } , D2 = { x x ≥−12 } , D3 ={ x x ≥− } 33
4
D = D1 ∩ D2 ∩ D3 = { x x ≥−5 }
x + 5 + x + 12 = 4x + 33 | ( )²
( )
2
x + 5 + x + 12 = 4x + 33
( )( )
x + 5 + 2 x + 5 x + 12 + x + 12 = 4x + 33
2
2 x + 17x + 60 = 2x + 16
2
x + 17x + 60 = x + 8 | ( )²
2
x
2
+ 17x + 60 = x + 16x + 64
x = 4
Probe: LS: 4 + 5 + 4 + 12 = 9 + 16 = 7
RS: 4 ⋅ 4 + 33 = 49 = 7
L = {4}