x²+y²=8
(x+y)/xy=1
Notam x+y=s
xy=p
sistemul devine
s²-2p=8
s=p
p²-2p-8=0
p1,2=(2+-√(4+32)) /2
p1,2=(2+-6)/2
p1=-2=s1
p2=4=s2
pt p1=s1=-2
construim ecuatia
z²+2z-2=0 care nu are radacni reale Δ=4-8=-4<0
(are 2 solutii complexe)
pt p2=s2=4
construim ecuatia
z²-4z+4=0
(z-2)²=0
care are radacinile z1=z2=2
decix1=y1=2
x2=y2=2
deci solutie unica in R x=y=2
