Question

Am nevoie neapărat, vă rog.
Rezolvați următorul sistem:
$\left \{ {{9+4xy-x-y=0} \atop {2x-3xy+2y-8=0}} \right.$

Answer 1

9+4xy-x-y = 0

2x-3xy+2y-8 = 0

-(x+y) + 4xy = -9

2(x+y) -3xy = 8

Notam x+y = S, xy = P

-S + 4P = -9 |•2

2S - 3P = 8

-2S + 8P = -18

2S - 3P = 8

5P = -10 => P = -2

=> 2S + 6 = 8 => S = 1=>

S = 1

P = -2

t²-St+P = 0

t²-t-2 = 0

Delta = 9 => t₁,₂ = (1±3)/2

=> (x,y) = { (-1,2) ; (2,-1) }