55. (3²)ˣ +2*3ˣ = 99
Notezi pe t = 3ˣ => t² +2t-99 = 0
delta = 4+4*99 = 4+396 = 400
t1 = (-2+20)/2 = 18/2 = 9
t2 =(-2-20)/2 = -22/2 = -11
din t1= 3ˣ => 9 = 3ˣ => 3² = 3ˣ => x = 2
t2 = 3ˣ=> -11 = 3ˣ (nu exista)
deci S={2}
56. a) (5-x)(6-x) = 56
30-5x-6x+x² = 56
x² -11x -26 = 0
delta = 121 +4*26 = 121 + 104 = 225
x1 = (11+15)/2 = 26/2 = 13 apartine N
x2 = (11-15)/2 = -4/2 = -2
=> S={13}
b) 2x+1 -(4-x)(5-x) = 720
2x+1 -(20-4x-5x+x²) = 720
2x+1 -(x² -9x+20)=720
2x+1 -x²+9x-20 -720 = 0
-x² +11x -739 = 0 /*(-1)
x² -11x+739 = 0
delta = 121 -2960 = -2835
x1, 2= (11+V-2835)/2 nu apartine R, deci nu exista solutii naturale
c) x-1 = 13/2
x = 13/2 +1 amplifici pe 1 cu 2
x = 13/2 +2/2
x = 15/2 nu apartine N
