Question

Решите систему уравнений : $left { {{x+y-7=0} atop {x^2+xy+y^2=43}} right.$

Answer 1

$displaystyle left { {{x+y-7=0} atop {x^2+xy+y^2=43}} right. Rightarrow left { {{x+y=7} atop {(x+y)^2-xy=43}} right. Rightarrow left { {{x+y=7} atop {7^2-xy=43}} right. \ \ \ left { {{x+y=7} atop {xy=6}} right. Rightarrow left { {{x=7-y} atop {(7-y)cdot y=6}} right. \ \ -y^2+7y=6\ y^2-7y+6=0$
По т. Виета:
$y_1=1\ y_2=6$
Тогда
$x_1=7-y_1=7-1=6\ x_2=7-y^2=7-6=1$


Ответ: $(6;1),,, (1;6).$