Question

Решите уравнние
Корень из 7-х²= корень из -6х

Answer 1

$sqrt{7-x^2}=sqrt{-6x}$
$left { {{7-x^2 geq 0} atop {-6x geq 0}} right.$
$left { {{x^2 leq 7} atop {x leq 0}} right.$
$left { {{x in [-sqrt7;sqrt7]} atop {xin(-infty;0]}} right.$
ОДЗ: $xin[-7;0]$
$|7-x^2|=|-6x|$
$left [ {{7-x^2=-6x} atop {7-x^2=6x}} right.$
$left [ {{x^2-6x-7=0} atop {x^2+6x-7=0}} right.$
$left[ x=pm1 atop x=pm7 right.$
С ОДЗ:
$left[ x=-1 atop x=-7 right.$
Ответ: -1; -7

Answer 2

возведем в квадрат
7-х^2=-6х
х^2-6х-7=0
д=36-4×1×(-7)=64
х1=(6-8)/2=-1
х2=(6+8)/2=7