Решите систему уравнений x^2+y^2=50. xy=50

[latex] \left \{ {{x^2+y^2=50,} \atop {xy=50;}} \right. \left \{ {{x^2+\frac{2500}{x^2}=50,} \atop {y=\frac{50}{x};}} \right. \left \{ {{x^4-50x^2+2500=0,} \atop {y=\frac{50}{x};}} \right. \\ x^2=a, \\ a^2-50a+2500=0, \\ D=(25)^2-1\cdot2500=-1875\ \textless \ 0, \\ a\in\varnothing, \\ x\in\varnothing,\\ y\in\varnothing.[/latex]