Question

Aflati numarul x nenul din:

Answer 1

8^14=(2³)^14=2^42
4 (1+2+..+x) =4^*(x*(x+1)/2)= (2²)^(x*(x+1)/2)=2^(x(x+1))
2^(x(x+1))=2^42
x(x+1) =42=6*7=6*(6+1)
x=6 verifica
x crescatoare, x+1 crescatoare, x(x+1) crescatoare
x=6, solutie unica

Answer 2

Suma Gauss   1+2+3+...+x=[x(x+1)]/2
4=2²   si    8=2³
2²⁽ˣ²⁺ˣ⁾/² = 2³ˣ¹⁴
2²⁽ˣ²⁺ˣ⁾/² = 2⁴²      bazele sun aceleasi, egalam puterile
2(x²+x)/2=42
x²+x=42
x²+x-42=0
a=1, b=1, c= - 42
Δ=b²-4ac=1²+168=169 > 0
x₁=( -1+13)/2=12/2=6 ∈  N
x₂=( -1-13)/2= -14/2= -7 ∉ N

Singura solutie convenabila este x = 6   ∈   N