√(3x+4) +√(5-4x) =4 | - √(5-4x)
√(3x+4) =4 - √(5-4x) |(...)^2
3x+4 = (4 - √(5-4x))^2
3x+4 = -4x+21 -8 √ (5-4x)) |+4x -21
7x -17 = -8 √ (5-4x)) (*-1)
17 -7x = 8 √ (5-4x) |(...)^2
(17 -7x)^2 = 64(5-4x)
49 x^2-238x +289 =320 -256x
49 x^2+18x -31 = 0 | :49
x^2+(18/49)x -31/49 = 0 ->pq-Formel z.B.
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x1= -1
x2= 31/49
Die Probe bestätigt die Richtigkeit der Lösungen