Question

determinati solutiile intregi ale inecuatiei radical din 16 +2x<x rad.5+ rad.20

Answer 1

$\it \sqrt{16} +2x<x\sqrt5+\sqrt{20} \Rightarrow 4+2x<x\sqrt5+2\sqrt5 \Rightarrow 2(x+2) < \sqrt5(x+2) \\ \\ \Rightarrow 2(x+2) -\sqrt5(x+2) <0 \Rightarrow (x+2)(2-\sqrt5)<0 \Rightarrow x+2>0\Rightarrow\\ \\ \Rightarrow x>-2\Rightarrow S+\{-1,\ 0,\ 1,\ 2,\ ...\}$