Question

решите систему уравнений:

а) {x^2+y^2=5

    {xy=2

 

в) {2x^2+3x^2+y^2=0

    {x^2-xy-y^2=4

 

б) {x^2-8xy+16y^2=25

     {4y^2-xy=5

 

г) {x^2-3xy+y^2=-1

    {8y^2-3xy=2

Answer 1

{x^2+y^2=5,

{xy=2;

 

x^2+2xy+y^2-2xy=5,

(x+y)^2-2xy=5;

(x+y)^2-2*2=5;

(x+y)^2=9;

 

[x+y=-3,

[x+y=3;

 

[y=-3-x,

[y=3-x;

 

[-x(3+x)=2,

[x(3-x)=2;

 

[x^2+3x+2=0,

[x^2-3x+2=0;

x_1=-2, x_2=-1, x_3=1, x_4=2,

y_1=-1, y_2=-2, y_3=2, y_4=1.

 

{x^2-8xy+16y^2=25,

{4y^2-xy=5;

 

{(x-4y)^2=25,

{y(4y-x)=5;

 

[x-4y=-5,

[x-4y=5;

 

-y(x-4y)=5,

[5y=5,

[-5y=5;

y_1=1, y_2=-1;

 

[x-4=-5,

[x-4*(-1)=5;

x_1=-1, x_2=1.