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4^1+2+3+...+X=2^14 aflați X

Răspuns :

4^(1+2+3+...+x)=2^14
2^[2×(1+2+3+...+x)]=2^14
2^[2×x×(x+1):2]=2^14
2^[x×(x+1)]=2^14

x×(x+1)=14
x^2+x-14=0
Δ=1-4×(-14)=1+56=57
x₁=(-1+√57)/2
x₂=(-1-√57)/2