Решите систему уравнений: х^2+у^2=18 ху=9

х^2+у^2=18 ху=9    x=9/y 81/y²+y²=18 y²=t 81+t²-18t=0   t²-18t+81=0  (t-9)²=0   t=9  y1=3   y2=-3                                                                  x1=3  x2=-3

[latex] \left \{ {{x^2+y^2=18} \atop {xy=9}} \right. \ \ \ \textless \ =\ \textgreater \ \ \ \left \{ {{x^2+y^2=18} \atop {x= \frac{9}{y} }} \right. \\ \\ (\frac{9}{y} )^2+y^2=18 \\ \\ \frac{81}{y^2} +y^2=18 \ \ |*y^2 \\ \\ 81+y^4=18y^2 \\ y^4-18y^2+81=0 \\ (y^2-9)^2=0 \\ y^2-9=0 \\ y^2=9 \\ \\ y_1=3 \\ y_2=-3 \\ \\ x_1= \frac{9}{y_1}= \frac{9}{3}=3 \\ x_2= \frac{9}{y_2}= \frac{9}{-3}=-3 \\ \\ OTBET: \ (3;3); \ (-3;-3)[/latex]