Question

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

Answer 1

( 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 )