Question

При каких значениях y имеет смысл выражение:
а) $\sqrt{2y-4} +\sqrt{5-\frac{y}{2} }$
б) $\sqrt{12-3y} +\frac{1}{\sqrt{y+2} }$

Answer 1

$1)\sqrt{2y-4}+\sqrt{5-\frac{y}{2}} \\\\\left \{ {{2y-4\geq 0} \atop {5-\frac{y}{2}\geq0 }} \right.\\\\\left \{ {{2y\geq4 } \atop {\frac{y}{2}\leq5}} \right.\\\\\left \{ {{y\geq2} \atop {y\leq 10}} \right.\\\\Otvet:\boxed{y\in[2;10]}$

$2)\sqrt{12-3y}+\frac{1}{\sqrt{y+2} }\\\\\left \{ {{12-3y\geq 0} \atop {y+2>0}} \right. \\\\\left \{ {{3y\leq12 } \atop {y>-2}} \right.\\\\\left \{ {{y\leq4 } \atop {y>-2}} \right. \\\\Otvet:\boxed{y\in(-2;4]}$