Question

Сумма двух чисел равна -2, а сумма их квадратов 3y. Найти эти числа

Answer 1

Объяснение:

$\left \{ {{x+y=-2} \atop {x^2+y^2=34}} \right. \ \ \ \ \ \left \{ {{(x+y)^2=(-2)^2} \atop {x^2+y^2=34}} \right.\ \ \ \ \ \left \{ {{x^2+2xy+y^2=4} \atop {x^2+y^2=34}} \right. \ \ \ \ \left \{ {{34+2xy=4\ |:2} \atop {x^2+y^2=34}} \right.\ \ \ \ \left \{ {{xy=-15} \atop {x+y=-2}} \right.$

$\left \{ {{(-y-2)*y=-15} \atop {x=-y-2}} \right. \ \ \ \ \left \{ {{-y^2-2y+15=0\ |*(-1)} \atop {x=-y-2}} \right. \ \ \ \ \left \{ {{y^2+2y-15=0} \atop {x=-y-2}} \right. \ \ \ \ \left \{ {{D=64\ \ \sqrt{D}=8 } \atop {x=-y-2}} \right.\ \ \ \ \left \{ {{y_1=-5\ \ y_2=3} \atop {x_1=3\ \ x_2=-5}} \right. .$

Ответ: (3;-5),   (-5;3).