Question

Найдите сумму корней уравнения V3-x + V6+x=3
(V - корень). Буду благодарна :)

Answer 1

$sqrt{3-x}+ sqrt{6+x} =3\ ========================\ left { {{3-x geq 0} atop {6+x geq 0}} right. \ left { {{-x geq -3} atop {x geq -6}} right. \ left { {{x leq 3} atop {x geq -6}} right. Rightarrow x in [-6;3] \ ========================\ (sqrt{3-x}+ sqrt{6+x})^2 =3^2\ 3-x+2 sqrt{(3-x)(6+x)}+6+x=9\ 2 sqrt{(3-x)(6+x)}=0\ sqrt{(3-x)(6+x)}=0\ 3-x=0 rightarrow x=3\ 6+x=0 rightarrow x=-6$

Ответ: x1 = 3; x2 = -6