Question

Subiectul 2 Ex 2 , va rog

Answer 1

(n^2-n-1)(n^2-n+1)+1 este patrat perfect?

Notam: n^2-n-1=t

Atunci n^2-n+1=(n^2-n-1)+2=t+2

Si avem:

t(t+2)+1=t^2+2t+1=(t+1)^2

Revenind la notatia initiala:

(n^2-n-1)(n^2-n+1)+1=( n^2-n-1+1)^2=(n^2-n)^2 care e patrat perfect.