x+y = 2 => x = 2-y
x·y = -15
((2-y)·y = -15
2y-y² =-15 /+15
2y - y² +15 =0 (este ecuatie de gradul al doilea)
-y² + 2y +15 = 0 /·(-1)
y² - 2y -15 = 0 (a=1 , b= -2 , c= -15)
Δ=b²-4ac = (-2)²-4·1·(-15) = 4 +60 = 64 ≥0
x₁,x₂=[tex] \frac{-b plus sau minus √Δ}{2a} [/tex]
= x₁=[tex] \frac{2+8}{2} = \frac{10}{2} =5[/tex]
x₂=[tex] \frac{2-8}{2} = \frac{-6}{2} = -3[/tex]
(x,y) ∈ {(5;-3),(-3;5)}
