Question

x+y=4 x2-y2=8 ...................................

Answer 1

Ответ:

x=2; y=2.

Пошаговое объяснение:

$\left \{ {{x+y=4} \atop {x^{2}+y^{2} =8}} \right.$

$\left \{ {{x=4-y} \atop {x^{2} +y^{2} =8}} \right.$

$\left \{ {{x=4-y} \atop {(4-y)^{2}+ y^{2}=8}} \right.$

$16-8y+y^{2} +y^{2} =8$

$2y^{2} -8y+16-8=0$ (:2)

$y^{2} -4y+4=0$

По т. Виета:

$\left \{ {{y_{1}+y_{2}=4} \atop {y_{1}*y_{2}=4}} \right.$  ⇒  $y=2$

$\left \{ {{x=4-y} \atop {y=2}} \right.$

$x=4-2$

$x=2.$

$\left \{ {{x=2} \atop {y=2}} \right.$

(2;2)