Question

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

Answer 1

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

Answer 2

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