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

[latex] left { {{x^2+y^2=50,} atop {xy=50;}} ight. left { {{x^2+frac{2500}{x^2}=50,} atop {y=frac{50}{x};}} ight. left { {{x^4-50x^2+2500=0,} atop {y=frac{50}{x};}} ight. \ x^2=a, \ a^2-50a+2500=0, \ D=(25)^2-1cdot2500=-1875 extless 0, \ ainvarnothing, \ xinvarnothing,\ yinvarnothing.[/latex]