Question

aratati ca n(n+1)(n+2)(n+3)=(n^2+3n+1)^2 ???

Answer 1

n(n+1)(n+2)(n+3)=(n²+3n+1)²
Inmultim prima cu ultima si a doua cu a treia:
(n²+3n)(n²+n+2n+2)=(n²+3n+1)²
(n²+3n)(n²+3n+2)=(n²+3n+1)²
Nptam n²+3n=a
a(a+2)=(a+1)²
a²+2a+1=(a+1)²
(a+1)²=(a+1)²
(n²+3n+1)²=(n²+3n+1)²