Question

решите систему уравнений х^2+у^2=10 ху=3

Answer 1

$left { {{x^2+y^2=10} atop {xy=3}} right. \ y= frac{3}{x} \ x^2 + ( frac{3}{x} )^2=10 \ x^2 + ( frac{3^2}{x^2} )=10 \ t=x^2 \ \ t + frac{9}{t} =10 \ t^2+9=10t \ t^2-10t+9=0 \ D/4=25-9=16 \ t=5б4 \ t_1=1; t_2=9 \ \ x^2=t \ x_{1,2} ^2=1;x_1=1; x_2=-1 \ x_{3,4} ^2=9;x_3=3; x_4=-3$

$y_{1,2} =б frac{3}{1} =б3 \ y_{3,4} =б frac{3}{3} =б1$

Ответ: (-1; -3); (1; 3); (-3; -1); (3; 1).