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Question Number 155164 by mnjuly1970 last updated on 26/Sep/21

$$solve..$$$$\lfloor \frac{x}{2+\sqrt{x}}\rfloor =3(x\in \mathbb{Z})$$$$$$

Answered by MJS_new last updated on 26/Sep/21

$$\frac{x}{2+\sqrt{x}}=3\Rightarrow x\approx 19.11$$$$\frac{x}{2+\sqrt{x}}=4\Rightarrow x\approx 29.85$$$$\frac{x}{2+\sqrt{x}}\mathrm{strictly}\mathrm{increasing}$$$$\Rightarrow \mathrm{answer}\mathrm{is}20⩽x⩽29$$

Commented by mnjuly1970 last updated on 26/Sep/21

$$bravo..perfect..$$

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