Question Number 155164 by mnjuly1970 last updated on 26/Sep/21
$$\:\:\:{solve}.. \\ $$$$\:\:\:\:\:\:\:\:\:\lfloor\:\frac{\:{x}}{\mathrm{2}+\:\sqrt{{x}}}\:\rfloor\:=\:\mathrm{3}\:\:\:\:\:\:\:\:\left(\:{x}\in\:\mathbb{Z}\:\right) \\ $$$$ \\ $$
Answered by MJS_new last updated on 26/Sep/21
$$\frac{{x}}{\mathrm{2}+\sqrt{{x}}}=\mathrm{3}\:\Rightarrow\:{x}\approx\mathrm{19}.\mathrm{11} \\ $$$$\frac{{x}}{\mathrm{2}+\sqrt{{x}}}=\mathrm{4}\:\Rightarrow\:{x}\approx\mathrm{29}.\mathrm{85} \\ $$$$\frac{{x}}{\mathrm{2}+\sqrt{{x}}}\:\mathrm{strictly}\:\mathrm{increasing} \\ $$$$\Rightarrow\:\mathrm{answer}\:\mathrm{is}\:\mathrm{20}\leqslant{x}\leqslant\mathrm{29} \\ $$
Commented by mnjuly1970 last updated on 26/Sep/21
$${bravo}\:\:..{perfect}.. \\ $$