СРОЧНО!!!
x^2-3xy+2y^2=0 , x^2+y^2=20 Система!

$left{ begin{array}{l} x^2 - 3xy + 2y^2 = 0 ; x^2 + y^2 = 20 . end{array}$

Решение:

При $y = 0$ и $x ,$ судя по первому уравнению, тоже должно быть равно нулю, а это не подходит во второе уравнение, значит $y neq 0$

$left{ begin{array}{l} x^2 - 3xy + 2y^2 = 0 || : y^2 ; x^2 + y^2 = 20 . end{array}$

$left{ begin{array}{l} frac{x^2}{y^2} - 3 frac{xy}{y^2} + 2 frac{y^2}{y^2} = frac{0}{y^2} ; x^2 + y^2 = 20 . end{array}$

$left{ begin{array}{l} ( frac{x}{y} )^2 - 3 frac{x}{y} + 2 = 0 ; Rightarrow D = 3^2 - 4 cdot 2 = 1^2 ; Rightarrow ( frac{x}{y} )_{12} = frac{ 3 - 1 }{2} = 1 ; ( frac{x}{y} )_{34} = frac{ 3 + 1 }{2} = 2 ; x^2 + y^2 = 20 . end{array}$

$left{ begin{array}{l} left[ begin{array}{l} x_{12} = y_{12} ; x_{34} = 2 y_{34} ; end{array} x^2 + y^2 = 20 . end{array}$

$left[ begin{array}{l} left{ begin{array}{l} x_{12} = y_{12} ; y_{12}^2 + y_{12}^2 = 20 ; end{array} left{ begin{array}{l} x_{34} = 2 y_{34} ; ( 2 y_{34} )^2 + y_{34}^2 = 20 . end{array} end{array}$

$left[ begin{array}{l} left{ begin{array}{l} x_{12} = y_{12} ; 2 y_{12}^2 = 20 ; end{array} left{ begin{array}{l} x_{34} = 2 y_{34} ; 4 y_{34}^2 + y_{34}^2 = 20 . end{array} end{array}$

$left[ begin{array}{l} left{ begin{array}{l} x_{12} = y_{12} ; y_{12}^2 = 10 ; end{array} left{ begin{array}{l} x_{34} = 2 y_{34} ; 5 y_{34}^2 = 20 . end{array} end{array}$

$left[ begin{array}{l} x_1 = y_1 = -sqrt{10} ; x_2 = y_2 = sqrt{10} ; left{ begin{array}{l} x_{34} = 2 y_{34} ; y_{34}^2 = 4 . end{array} end{array}$

$left[ begin{array}{l} ( x_1 ; y_1 ) = ( -sqrt{10} ; -sqrt{10} ) ; ( x_2 ; y_2 ) = ( sqrt{10} ; sqrt{10} ) ; left{ begin{array}{l} y_3 = -2 ; x_3 = -4 ; end{array} left{ begin{array}{l} y_4 = 2 ; x_4 = 4 . end{array} end{array}$

О т в е т :
$( x_1 ; y_1 ) = ( -sqrt{10} ; -sqrt{10} )$ .
$( x_2 ; y_2 ) = ( sqrt{10} ; sqrt{10} )$ .
$( x_3 ; y_3 ) = ( -2 ; -4 )$ .
$( x_4 ; y_4 ) = ( 2 ; 4 )$ .

или:

О т в е т : $( x ; y ) in { ( -sqrt{10} ; -sqrt{10} ) , ( sqrt{10} ; sqrt{10} ) , ( -4 , -2 ) , ( 4 , 2 ) }$ ;

или:

О т в е т : $( x ; y ) in { ( pm sqrt{10} ; pm sqrt{10} ) , ( pm 4 , pm 2 ) } .$