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x-Z-A-R-A-4-3-x-4-x-




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

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