Question

rezolvați inecuația combinări de 17 luate cate x ≤combinari de 17 luate cate x-2​

Answer 1

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