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Răspunsuri la întrebare
1. C₃² = 3! /(2!*1!) =(2!*3) / 2! = 3
3! = 1*2*3 = 6
3+6 = 9
2. A₄⁴ = 4! /(4-4)! = 4!/0! = 1*2*3*4 = 24
C₄⁴ = 4! /(4!*0!) = 4!/ 4! = 1
24+1 = 25
3. Cₙ² = n! /(2!*(n-2)!) = (n-2)!(n-1)n /(n-2)!*2 = (n-1)n /2 = (n²-n)/2
(n²-n)/2 = 28 ⇒ n²-n = 56 ⇒ n²-n-56 = 0
Δ = 1+224 = 225
n₁ = (1+15)/2 = 16/2 = 8
n₂ = (1-15)/2 = -14/2 = -7 ∉ N
n={8}
4. C₅² = 5! /2!*3! = (3!*4*5) /3!*2 = 10
5. A₆² = 6! /4! = (4!*5*6) /4! = 30
C₆⁴ = 6! /(4!*2!) = (4!*5*6)/ (4!*2) = 15
30 -2*15 = 30-30 = 0
6. C₄² = 4! /(2!*2!) = (2!*3*4)/(2!*2) = 6
7. Aₙ¹ = n
Cₙ¹ = n
n+n = 10 ⇒ 2n = 10 ⇒ n = 5
8. (n-3)! /(n-5)! = (n-3)(n-4)(n-5)........ / (n-5)(n-6)(n-7).... = (n-3)(n-4)
n²-7n+12= 6
n²-7n+6 = 0
Δ = 49 -24 = 25
n₁ = (7+5)/2 = 12/2 = 6
n₂ = (7-5)/2 = 2/2 = 1
Din n ∈ [5, infinit) ⇒ n={6}