Question

Aflati numerele naturale n,astfel incat : a) 8 supra n+2 >_ 6 supra 11 ; b) 9 supra 16 <_ 5 supra 3n + 1 <_ 3 supra 4.

Answer 1

a)8/(n+2)≥6/11 |×(n+2)
8≥[6(n+2)]/11
8≥(6n+12)/11 ×11
88≥6n+12
88-12≥6n
76≥6n
76/6≥n
38/3≥n =>n≤38/3 (≈12,(6)≈12,66)
b)9/16≤5/(3n+1) |×(3n+1)
[9(3n+1)]/16≤5
(27n+9)/16≤5 |×16
27n+9≤80
27n≤80-9
27n≤71
n≤71/27 (≈2,62)