Răspuns:
19.
E(x) = 6x²-4x+9x-6-(x²+1-2x)-(4x²+1-4x)+26 =
= 6x²-4x+9x-6-x²-1+2x-4x²-1+4x+26 =
= x²+11x+18
E(7ⁿ-2) = (7ⁿ-2)²+11(7ⁿ-2)+18 =
= 7²ⁿ+4-4·7ⁿ+11·7ⁿ-22+18 =
= 7²ⁿ+7·7ⁿ =
= 7²ⁿ+7ⁿ⁺¹ =
= 7ⁿ⁺¹(7ⁿ⁻¹-1)
⇒ E(7ⁿ-2) - divizibil cu 7ⁿ⁺¹ (∀) n∈N*
21.
E(x) = 4x²+9+12x-(2²-x²)-5x²-12x =
= 4x²+9+12x-4+x²-5x²-12x =
= 5
E(x) = 5, (∀) x∈R
E(2020) = 5
⇒ E(x) = E(2020) = E(2021)
