Question

Rezolvati ecuatiile in N 100 puncte raspuns corect

Answer 1

Răspuns:

Explicație pas cu pas:

a) Cₓ₋₃³ = x-3 ; x-3 ≥ 3 => x ≥ 6

Cₓ₋₃³ = x-3 <=> (x-3)! /[3!·(x-6)!] = x-3 <=>

(x-6)!(x-5)(x-4)(x-3)/[6·(x-6)! ] = x-3 <=>

(x-5)(x-4)(x-3) = 6(x-3) =>

(x-5)(x-4) = 6 <=>

x²-9x+14 = 0 => x₁,₂ = (9±√(81-56)]/2 = (9±5)/2

x₁ = 2 , nu convine ; x₂ = 7 = solutie

b) n! /(n-2)! = 56 <=>

n·(n-1)·(n-2)! /(n-2)! = 56 <=>

n·(n-1) = 56 <=>

produsul a doua numere consecutive = 56 <=>

8·7 = 56 =>

n = 8