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Determina numarul natural n: 5^n+5^(n+1)+5^(n+2)=775

Răspuns :

Vilmaristul
5ⁿ(1+5+25)=5²*31
5ⁿ*31=5²*31 se simplifica cu 31
5ⁿ=5²
n=2
5^n+5^(n+1)+5^(n+2)=775
5^n+5^n*(5+1)+5^n*(5^2+1)=775
5^n+5^n*6+5^n*(25+1)=775
5^n+5^n*6+5^n*26=775
5^n*(1+6+26)=775
5^n*33=775
5^n=775:33
5^n=25
n=2

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