Question

17. Determinaţi numerele naturale n care verifică relaţiile: a) 1pe3<npe12<3pe4; b)1pe9<1pe2n+1<1


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Answer 1

Explicație pas cu pas:

a)

$\frac{1}{3} < \frac{n}{12} < \frac{3}{4} \iff \frac{4}{12} < \frac{n}{12} < \frac{9}{12} \\ \iff 4 < n < 9 \implies \bf n \in \{5 ; 6 ; 7 ; 8\}$

b)

$\frac{1}{9} < \frac{1}{2n + 1} < 1 \iff \frac{1}{9} < \frac{1}{2n + 1} < \frac{1}{1} \\ \iff 9 > 2n + 1 > 1 \iff 8 > 2n > 0 \\ \implies 4 > n > 0 \implies \bf n \in \{1 ; 2 ; 3\}$