Question

6x+|4-x^2|=3

найти сумму корней уравнения

Answer 1

$6x+|4-x^2|=3$
1) $left { {{4-x^{2} geq 0} atop {6x+4-x^2=3}} right.$
$left { {{-2 leq x leq 2} atop {x^2-6x-1=0, D=40}} right.$
$left { {{-2 leq x leq 2} atop {x_{1}= frac{6- sqrt{40}}{2}, x_{2}= frac{6+sqrt{40}}{2}}} right.$
$left { {{-2 leq x leq 2} atop {x_{1}=3- sqrt{10}, x_{2}=3+sqrt{10}} right.$
$x= 3-sqrt{10}$ - корень

2) $left { {{4-x^{2}leq0} atop {6x-4+x^2=3}} right.$
$left { {{x leq -2, x geq 2} atop {x^2+6x-7=0, D=64}} right.$
$left { {{x leq -2, x geq 2} atop {x_{3}=-7, x_{4}=1}} right.$
$x=-7$ - корень

Сумма корней: $3-sqrt{10}-7=-4-sqrt{10}$