{x^2+y^2-xy=3
{x+y-3xy=-3
{(x+y)²-3xy=3
{(x+y)-3xy=-3
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(x+y)²-(x+y)=6
(x+y)²-(x+y)-6=0
D=25=5²
1)
x+y=(1+5)/2=3
y=3-x
x+3-x-3(3-x)x=-3
3-9x+3x²+3=0
3x²-9x+6=0
x²-3x+2=0
D=1
x₁=(3-1)/2=1
y₁=2
x₂=(3+1)/2=2
y₂=1
2)
x+y=(1-5)/2=-2
y=-x-2
x+y-3xy=-3
x-x-2-3x(-x-2)=-3
-2+3x²+6x+3=0
3x²+6x+1=0
D=36-12=24=4*6
x₃=(-6-2√6)/6=-1-√6 /3=-1-√(2/3)
y₃=-x-2=1+√(2/3)-2=√(2/3)-1
x₄=-1+√(2/3)
y₄=1-√(2/3)-2=-1-√(2/3)