Question

3. Determinati valorile lui n e N pentru care avem:

Ex 3

Answer 1

Ai răspuns atașat pe foaie.

Answer 2

Explicație pas cu pas:

a)

$\frac{3}{5} < \frac{n}{12} < \frac{14}{15} \\ \frac{3 \times 12}{5} < n < \frac{14 \times 12}{15} \\ \frac{36}{5} < n < \frac{56}{5} \\ 7 \frac{1}{5} < n < 11 \frac{1}{5}$

=> n ∈ {8; 9; 10; 11}

b)

$\frac{2}{7} < \frac{n}{56} < \frac{3}{8} \\ \frac{2 \times 56}{7} < n < \frac{3 \times 56}{8} \\ 16 < n < 21$

=> n ∈ {17; 18; 19; 20}

c)

$\frac{2}{5} < \frac{n}{30} < \frac{1}{2} \\ \frac{2 \times 30}{5} < n < \frac{30}{2} \\ 12 < n < 15$

=> n ∈ {13; 14}

d)

$\frac{2}{3} < \frac{54}{n} < \frac{9}{13} \\ \frac{3}{2} > \frac{n}{54} > \frac{13}{9} \\ \frac{3 \times 54}{2} > n > \frac{13 \times 54}{9} \\ 81 > n > 78$

=> n ∈ {79; 80}

e)

$\frac{14}{29} < \frac{6}{n} < \frac{7}{12} \\ \frac{29}{14} > \frac{n}{6} > \frac{12}{7} \\ \frac{29 \times 6}{14} > n > \frac{12 \times 6}{7} \\ \frac{87}{7} > n > \frac{72}{7} \\ 10 \frac{2}{7}< n < 12 \frac{3}{7}$

=> n ∈ {11; 12}

f)

$\frac{5}{3} < \frac{35}{n} < \frac{7}{3} \\ \frac{3}{5} > \frac{n}{35} > \frac{3}{7} \\ \frac{3 \times 35}{5} > n > \frac{3 \times 35}{7} \\ 21 > n > 15$

=> n ∈ {16; 17; 18; 19; 20}