Question

rezolvati sistemul de ecuatie :$\left \{ {{x+y=5} \atop {xy=6}} \right.$

Answer 1

x+y=5=S
xy=6=P
 x²-Sx+P=0
x²-5x+6=0
Δ=b²-4ac=25-24=1
x₁,₂=$= \frac{-b+/- \sqrt{delta} }{2a} = \frac{5+/-1}{2}$
x₁=$\frac{5+1}{2}=3$
x₂=$\frac{5-1}{2}=2$
  x₁+y₁=5⇒y₁=5-x₁=5-3=2
  x₂+y₂=5⇒y₂=5-x₂=5-2=3
(x,y)∈{(3,2);(2,3)}