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aratati ca a =(3^21+3^20+3^19)/39 este patrat perfect rezultat (3^9)^2 cum se rezolva?


Răspuns :

[tex]a=3^{18}(3^3+3^2+3^1)/39\\ a=3^{18}*39/39\\ a=3^{18}=(3^9)^2=\ \textgreater \ a\ p.p.[/tex]
a=3^19(3^2+3^1+1) / 39
a=3^19(9+3+1)/39
a=3^19 * 13 / 39
a=3^19 * 13 / 3*13
a=3^18 * 1
a=(3^9)^2