Question

Rezolvați ecuația (n+2)! +18n! = 10 (n+1)!

Answer 1

(n+2)! +18n! = 10 (n+1)n!   , n>0

(n+2)(n+1)n!+18n!=10(n+1)n!        :n!

(n+2)(n+1)+18=10(n+1)

n²+3n+2+18-10n-10=0

n²-7n+10=0

Δ=49-40=9

n1=(7+3):2=5

n2=(7-3):2=2

n={2,5}