Question

aratati ca numarul a=(3^21+3^20+3^18):37 este patrat perfect si cub perfect

Answer 1

a=3^18 (3^3 + 3^2 + 1) : 37 =

3^18 (27+9+1) : 37 =

3^18 = (3^9)^2 = (3^6)^3 deci si pp si cp.

Answer 2

a = ( 3²¹ + 3²⁰ + 3¹⁸ ) : 37

a = ( 3¹⁸ x 3³ + 3¹⁸ x 3² + 3¹⁸ x 1 ) : 37

a = 3¹⁸ x ( 3³ x 3² x 1 ) : 37

a = 3¹⁸ x ( 27 + 9 + 1 ) : 37

a = 3 ¹⁸ x 37 : 37

a = 3¹⁸ = ( 3⁹ )² → patrat perfect

a =3 ¹⁸ =  ( 3⁶ ) ³ → cub perfect