Question

Calculati : 3(n+2)!+5(n+1)!=52n! .. Va rog ajutati-ma , maine dau lucrare si am nevoie de ajutor.

Answer 1

3(n+2)(n+1)n!+5(n+1)n!=52n!
3(n+2)(n+1)+5(n+1)=52
3(n²+3n+2)+5(n+1)=52
3n²+9n+6+5n+5-51=0
3n²+14n-40=0
Δ=14²+3*4*40=676

$n_{1}= \frac{-14+ \sqrt{676} }{6}= 2$

$n_{2}= \frac{-14- \sqrt{676} }{6}= -6.(6)$ Care nu ne convine deoarece n∈N

deci n=2