Question

x+4xy+y=6
x^2y+xy^2=2
это система
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Answer 1

$x+4xy+y=6\ x^2y+xy^2=2\ \ x+y+4xy=6\ xy(x+y)=2\ \ x+y=6-4xy\ xy(6-4xy)=2\ \ xy=t\ 6t-4t^2=2\ 4t^2-6t+2=0\ D=36-4*4*2=2^2 t_{1}=frac{6+2}{8}=1\ t_{2}=frac{6-2}{8}=frac{1}{2}\ xy=1\ xy=0.5$

$xy=1\ xy=0.5\ \ 1)\ x+4xy+y=6\ xy=1\ \ x=frac{1}{y}\ frac{1}{y}+4+y=6\ 4y+y^2-6y+1=0\ y^2-2y+1=0\ (y-1)^2=0\ y=1\ x=1\ \ 2)\ x+4xy+y=6\ xy=0.5\ \ x=frac{0.5}{y}\ frac{0.5}{y}+4*0.5+y=6\ 0.5+2y+y^2-6y=0\ y^2-4y+0.5=0\ D=sqrt{56}\ y_{1}=-frac{sqrt{14}-4}{2}\ y_{2}=frac{sqrt{14}+4}{2}\ x_{1}=-frac{sqrt{14}+8}{4sqrt{14}-18}\ x_{2}=-frac{ sqrt{14}-8}{4sqrt{14}+18}$