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aratati ca numarul c=(4la50+4la49+4la48):21 este patrat perfect si cub perfect

Răspuns :

[tex]c=(4^{50}+4^{49}+4^{48}):21\\ c=4^{48}(1+4+4^2):21\\ c=4^{48}(5+16):21\\ c=4^{48}*21:21\\ c=4^{48}\\ c=4^{48}=(4^{24})^2=\ \textgreater \ c=patrat\ perfect\\ c=4^{48}=(4^{16})^3=\ \textgreater \ c=cub\ perfect[/tex]