Răspuns:
Explicație pas cu pas:
C₁₇ˣ ≤ C₁₇ˣ⁻² ; x ∈ N ; x ≥ 2 =>
17! /[x! ·(17-x)!] ≤ 17! / [(x-2)!·(17-x+2)!] =>
1/[(x!·(17-x)!] ≤ 1/[(x-2)!·(17-(x-2))!] <=>
(x-2)!·[17-(x-2)]! ≤ x!·(17-x)! =>
(x-2)!·[17-(x-2)]·[17-(x-1)]·(17-x)! ≤ x·(x-1)(x-2)!·(17-x)! =>
[17-(x-2)]·[17-(x-1)] ≤ x·(x-1) <=>
(19-x)(18-x) ≤ x·(x-1) =>
342 -37x+x² ≤ x²-x =>
342 ≤ 36x => x ≥ 342/36 =>
x ≥ 19/2 => x ≥ 10 I x ∈ N
