Question

Va rog mult am nevoie de ajutor la exercițiile astea doua!!!​

Answer 1

Răspuns:

Explicație pas cu pas:

18)

A = {x ∈ N  I 8ˣ + 8ˣ⁺¹ = patrat perfect}

8ˣ + 8ˣ⁺¹ = 8ˣ+8·8ˣ = 8ˣ(1+8) = 8ˣ·9 = 3²·8ˣ =>

x = {0 ; 2 ; 4 ; 6.....} => A = 2n ; n ∈ N  

B = { x ∈ N  I 24ˣ+24ˣ⁺¹ =  patrat perfect}

24ˣ+24ˣ⁺¹ =  24ˣ+24·24ˣ = 24ˣ(1+24) = 25·24ˣ = 5²·(2³·3)ˣ=>

= > x = {0 ; 2 ; 4 ; 6....}  => B = 2n ; n ∈ N

A , B = orice numar natural par

19)

A = { x ∈ N  I 7 ≤ x ≤ 11} => A = {7 ; 8 ; 9 ; 10 ; 11}

B =  {x ∈ N  I 5 ≤ x-2 ≤ 9}

5 ≤ x-2 ≤ 9 <=> 5+2 ≤ x ≤ 9+2 => B = {7 ; 8 ; 9 ; 10 ; 11}

C =  {x ∈ N  I 13 ≤ 2x-1 ≤ 21}

13 ≤ 2x-1 ≤ 21 => 13+1 ≤ 2x ≤ 21+1 => 14 ≤ 2x ≤ 22 =>

7 ≤ x ≤ 11 => C = {7 ; 8 ; 9 ; 10 ; 11} =>

A = B = C = {7 ; 8 ; 9 ; 10 ; 11}