Question

Sa se rezolve ecuația

Answer 1

(n+2)!/n!=56; n ∈ N

(n+2)(n+1)•n!/n!=56

(n+2)(n+1)=8•7 =>n=6

sau n²+3n+2-56=0

n²+3n-54=0

Δ=9+216=225

n1=(-3+15)/2=6

n2=(-3-15)/2=-9, nu convine

=> n=6

Answer 2

(n+2)!/n!=56

(n+2)×(n+1)×n!/n!=56 - simplificam cu n!

(n+2)×(n+1)=56

(n+2)×(n+1)=8×7

n+2=8 ⇒ n=8-2 ⇒ n=6

n+1=7 ⇒ n=7-1 ⇒ n=6