Помогите решить систему уравнений,пожалуйста {x/y+y/x=5/2 {x^2+y^2=20

( Х/y ) + ( y/x ) = 5/2 ( x^2 + y^2 )/xy = 5/2 2( x^2 + y^2 ) = 5xy x^2 + y^2 = 2,5xy ••••••••• X^2 + y^2 = 20 20 = 2,5xy x = 8/y •••••••••• X^2 + y^2 = 20 ( 8/y)^2 + y^2 = 20 ( 64/ y^2 ) + y^2 = 20 64 + y^4 = 20y^2 y^2 = a ; a > 0 a^2 - 20a + 64 = 0 D = 400 - 256 = 144 = 12^2 a1 = ( 20 + 12 ) : 2 = 16 a2 = ( 20 - 12 ) : 2 = 4 •••••••••• y^2 = a y^2 = 16 ; y1 = 4 ; y2 = - 4 y^2 = 4 ; y3 = 2 ; y4 = - 2 ••••••••••••• X = 8 / y X1 = 8 / 4 = 2 X2 = 8 / - 4 = - 2 X3 = 8 / 2 = 4 X4 = 8 / - 2 = - 4 Ответ ( 2 ; 4 ) ; ( - 2 ; - 4 ) ; ( 4 ; 2 ) ; ( - 4 ; - 2 )