Question

Как решить (3-sqrt(10-x))(sqrt(x)-2) < 0?

Answer 1

$(3-\sqrt{10-x})(\sqrt{x}-2)<0\; ,\; \; ODZ:\; \left \{ {{10-x\geq 0} \atop {x\geq 0}} \right. \; \left \{ {{x\leq 10} \atop {x\geq 0}} \right. \; \to \; 0\leq x\leq 10\\\\a)\; \; \left \{ {{3-\sqrt{10-x}>0} \atop {\sqrt{x}-2<0}} \right. \; \left \{ {{\sqrt{10-x}<3} \atop {\sqrt{x}<2}} \right. \; \left \{ {{10-x<9} \atop {x<4}} \right. \; \left \{ {{x>1} \atop {x<4}} \right. \; \left \{ {{1<x<4} \atop {0\leq x\leq 10}} \right. \; \to \; 1<x<4$

$b)\; \; \left \{ {{3-\sqrt{10-x}<0} \atop {\sqrt{x}-2>0}} \right. \; \left \{ {{\sqrt{10-x}>3}} \atop {\sqrt{x}>2}} \right. \; \left \{ {{10-x>9} \atop {x>4}} \right. \; \left \{ {{x<1} \atop {x>4}} \right. \; \; \to \; \; x\in \varnothing \\\\Otvet:\; \; x\in (1,4)\; .$