Question

решите систему х^2-4ху+4у^2=25 х+2у=3​

Answer 1

$\left \{ {{x^2-4xy+4y^2=25} \atop {x+2y=3}} \right.$

$\left \{ {{(x-2y)^2=25} \atop {x+2y=3}} \right.$

$\left \{ {{(x-2y)^2-25=0} \atop {x+2y=3}} \right.$

$\left \{ {{(x-2y)^2-5^2=0} \atop {x+2y=3}} \right.$

$\left \{ {{(x-2y-5)(x-2y+5)=0} \atop {x+2y=3}} \right.$

$\left \{ {{(x-2y-5)(x-2y+5)=0} \atop {x=3-2y}} \right.$

$\left \{ {{3-2y-2y-5=0} \atop {3-2y-2y+5=0}} \right.$

$1)3-2y-2y-5=0$

 $-4y-2=0$

   $y_1=-0,5$

   $x_1=3-2*(-0,5)=4$

   $x_1=4$

$2)3-2y-2y+5=0$

  $-4y+8=0$

    $y_2=2$

    $x_2=3-2*2=-1$

   $x_2=-1$

Ответ:  {4;  -0,5};   {-1;  2}