Решите систему уравнений : x+y=20 x^2+y^2=20

$\left \{ {{x+y=20} \atop {x^2+y^2=20}} \right.\; \left \{ {{(x+y)^2=400} \atop {x^2+y^2=20}} \right. \; \left \{ {{(x^2+y^2)+2xy=400} \atop {x^2+y^2=20}} \right. \; \left \{ {{20+2xy=400} \atop {x^2+y^2=20}} \right. \\\\ \left \{ {{2xy=380} \atop {x^2+y^2=20}} \right. \; \left \{ {{xy=190} \atop {x^2+y^2=20}} \right. \; \left \{ {{y=\frac{190}{x}} \atop {x^2+y^2=20}} \right. \\\\x^2+\frac{190^2}{x^2}=20\; |\cdot x^2\; (x\ne 0)\\\\x^4+190^2=20x^2\\\\t=x^2\; \; \Rightarrow \quad t^2-20t+36100=0$

$D=400-4\cdot 36100\ \textless \ 0\; \; \; \Rightarrow \quad net\; \; dejstvit.\; \; reshenij$

Система не имеет решений