Question

se consideră expresia

​

Answer 1

Răspuns:

E(x)= 5$x^{2}$+30x+x+6+($x^{2}$-1)($x^{2}$+1)-($x^{4}$+4$x^{2}$+4)-30x

E(x)= 5$x^{2}$+x+6+$x^{4$-1-$x^{4$-$4x^{2}$-4

E(x)=$x^{2}$+x+1

E(n)=$n^{2}$+n+1

$n^{2} < n^{2} +n+1 < ( n+1)^{2}$  "A", n∈N

b) Conform a), E(n) este cuprins intre doua numere consecutive⇒ E(n) nu poate fi patrat perfect ⇒ n∈∅