Question

Aratati ca d = ( 4⁵⁰ + 4⁴⁹ + 4⁴⁸ ) : 21 este patrat perfect si cub perfect.

Answer 1

$d=(4^{50}+4^{49}+4^{48}):21$

$d=4^{48}*(4^2+4^1+4^0):21$

$d=4^{48}*(16+4+1):21$

$d=4^{48}*21:21$

$d=4^{48}$

$d=(4^{24})^2$ -demonstreaza ca e patrat perfect

$d=(4^{16})^3$ -demonstreaza ca e cub perfect