Question

Найти корень уравнения √-30-2х=-19-х

Answer 1

$\sqrt{-30 - 2x} = - 19 - x \\ \left \{ {{-30 - 2x \geq 0} \atop {-30 - 2x=(- 19 - x)^{2} }} \right. \\ \left \{ {{- 2x \geq 30} \atop {-30 - 2x= (-1)^{2}*(19 + x)^{2} }} \right. \\ \left \{ {{x \leq - 15} \atop {-30 - 2x= (19 + x)^{2} }} \right. \\ \left \{ {{x \leq - 15} \atop {-30 - 2x= 361 + 38x+ x^{2} }} \right. \\ \left \{ {{x \leq - 15} \atop {x^{2}+ 40x+391 = 0}} \right.$

$D=1600 - 4*391 = 1600 - 1564 = 36 \\ \sqrt{D} = 6 \\ x1 = - 17 ; x2 = - 23$


Оба корня удовлетворяют условию Х ≤ 15

Ответ:  -17;  -23