Question

Решите систему уравнений {y-x=12;
{y-x=xy/360​

Answer 1

{y-x=12 {x=y-12 {x=y-12 {y-x=xy/360 {y-y-12=y-12*y/360 {-12=y-2*y/360 x=y-y-2*y/360=y-(-12) x=-2*y/360=y+12 x=y+12=2*y/360 y=x-12 {x-12-y+12=12 {x-y=12 {x-12-y+12=((y+12)(x-12))/360 {x-y=xy/360

Answer 2

$\left \{ {{y-x=12} \atop {y-x=\frac{xy}{360} }} \right.$

$\left \{ {{y-x=12} \atop {12=\frac{xy}{360} }} \right.$

$\left \{ {{y-x=12} \atop {xy=12*360 }} \right.$

$\left \{ {{y=x+12} \atop {xy=4320 }} \right.$

$\left \{ {{y=x+12} \atop {x*(x+12)=4320 }} \right.$

$x*(x+12)=4320$

$x^2+12x-4320=0$

$D=144-4*1*(-4320)=144+17280=17424=132^2$

$x_1=\frac{-12-132}{2}= \frac{-144}{2}=-72$

$x_2=\frac{-12+132}{2}= \frac{120}{2}=60$

$x_1=-72 ==>y_1=-72+12=-60$

    $(-72;-60)$

$x_2=60 ==>y_1=60+12=72$

    $(60;72)$

Ответ:  (-72;  -60);    (60;  72)