Question

Aratati ca nr n=3^23•4^23-2^21•6^23 este patratul unui nr nat

Answer 1

n = 3²³ x 4²³ - 2²¹ x 6²³

n = ( 3 x 4 )²³ - ( 2 x 6 )²¹  x 6²

n = 12²³ - 12²¹ x 6²

n = 12²¹ x ( 12² - 6² )

n = ( 4 x 3 ) ²¹ x 6² x ( 2² - 1 )

n = 4²¹ x 3²¹ x 6² x 3

n = ( 2²¹ ) ² x 3²² x 6²

n = ( 2²¹ x 3¹¹ x 6 ) ²

n = [ ( 2 x 3)¹¹ x 2¹⁰ x 6 ]²

n = ( 6¹² x 2¹⁰) ²

n = ( 12¹⁰ x 6² )² → patrat perfect