5x+5y=2xy+11 |*2 => 10x+10y - 4xy = 22
3x+3y+4xy=17
------------------------- (+)
13x+13y = 39
=> x+y = 3
5x+5y-2xy = 11 => 5(x+y)-2xy = 11 => 15-2xy = 11 => 2xy = 4 => xy = 2
3x+3y+4xy = 17 => 3(x+y)+4xy = 17 => 9 + 4xy = 17 => 4xy = 8 => xy = 2
x+y = 3
xy = 2
t^2 - (x+y)t +xy = 0 => t^2-3t+2 = 0
Delta = 9 - 8 => t1,2 = (3±1)/2 => t1 = 1, t2 = 2
=> (x,y) = {(1,2);(2,1)}
=> (x1,y1) = (1,2); (x2,y2) = (2,1);
=> x1+x2 = 1+2 = 3
=> Raspuns corect c)
x1+x2 se afla in intervalul (0,3]
