Question Number 10232 by konen last updated on 30/Jan/17
$$\mathrm{x}\in\mathrm{Z},\:\mathrm{A}\in\mathrm{R} \\ $$$$\mathrm{A}=^{\mathrm{4}} \sqrt{\mathrm{3}−\mid\mathrm{x}−\mathrm{4}\mid}\:\Rightarrow\Sigma\mathrm{x}=? \\ $$
Answered by mrW1 last updated on 30/Jan/17
$${A}\in{R}\:\Rightarrow\:\mathrm{3}−\mid{x}−\mathrm{4}\mid\geqslant\mathrm{0} \\ $$$$\mid{x}−\mathrm{4}\mid\leqslant\mathrm{3} \\ $$$$−\mathrm{3}\leqslant{x}−\mathrm{4}\leqslant\mathrm{3} \\ $$$$\mathrm{1}\leqslant{x}\leqslant\mathrm{7} \\ $$$${since}\:{x}\in{Z}\:\Rightarrow\:\Sigma{x}=\underset{{i}=\mathrm{1}} {\overset{\mathrm{7}} {\sum}}{i}=\frac{\mathrm{7}×\mathrm{8}}{\mathrm{2}}=\mathrm{28} \\ $$