Question

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

Answer 1

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