Запишите пересечение заданных множеств А и В, если А={х|х+3 < 0}, В={х|x² + 6х - 16 ≤ 0}.

Question

Запишите пересечение заданных множеств А и В, если А={х|х+3 < 0}, В={х|x² + 6х - 16 ≤ 0}.

Answer 1

Решаем неравенства:
\\ \left \{ {{x-2 <=0} \atop {x+8 >=0}} \right. \ \ \ \ \ \ \left \{ {{x-2 >=0} \atop {x+8 <=0}} \right. \\ \left \{ {{x <=2} \atop {x >=-8}} \right. \ \ \ \ \ \ \left \{ {{x >=2} \atop {x <=-8}} \right. \\ x \in [-8;2]\ \ \ \ \ \ \ \ x=\varnothing\\ \\ A= (\infty;-3)\\ B=[-8;2]\\ A \cup B = (-\infty;2]\\ A \cap B = [-8;-3) " alt="A.\\ x+3<0\\ x<-3\\ B.\\ x^2+6x-16<=0\\ D=36+4*16=100\\ x_1=\frac{-6+10}{2}=2\\ x_2=\frac{-6-10}{2}=-8\\ x^2+6x-16<=0\\ (x-2)(x+8)<=0\\ =>\\ \left \{ {{x-2 <=0} \atop {x+8 >=0}} \right. \ \ \ \ \ \ \left \{ {{x-2 >=0} \atop {x+8 <=0}} \right. \\ \left \{ {{x <=2} \atop {x >=-8}} \right. \ \ \ \ \ \ \left \{ {{x >=2} \atop {x <=-8}} \right. \\ x \in [-8;2]\ \ \ \ \ \ \ \ x=\varnothing\\ \\ A= (\infty;-3)\\ B=[-8;2]\\ A \cup B = (-\infty;2]\\ A \cap B = [-8;-3) " align="absmiddle" class="latex-formula">