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Aratati ca nr d=(4^50+4^49+4^48):21 este patrat si cub perfect

Răspuns :

(4⁵⁰ + 4⁴⁹ + 4⁴⁸) : 21 =

= 4⁴⁸(4² + 4 + 1) : 21

= 4⁴⁸(16 + 4 + 1) : 21

= 4⁴⁸·21 : 21

= 4⁴⁸

4⁴⁸ = (4²⁴)² = patrat perfect

4⁴⁸ = (4¹⁶)³ = cub perfect