Question

Решите систему уравнений Х^2+у^2=73 Ху=-24

Answer 1

$\left \{ {{x^2+y^2=73} \atop {x*y=-24}} \right.\\ \left \{ {{ \frac{576}{x^2} +x^2=73} \atop {y= \frac{-24}{x} }} \right.\\ \left \{ {{576+x^4-73x^2=0} \atop {y= \frac{-24}{x} }} \right. \\ x^4-73x^2+576=0\\x^2=a\bigg|(a\ \textgreater \ =0)\\a^2-73a+576=0\\D^2=(-73)^2-4*576 =3025;\sqrt{D}=\pm55\\-55 \neq x^2\\ x^2=55\\x=\pm\sqrt{55}\\ \left \{ {{x=\pm\sqrt55} \atop {y= \frac{-24}{\pm\sqrt55} }} \right.$