Question

Aflati ca numarul n=3^23•4^23-2^21•6^23 este patrat perfect

Answer 1

Răspuns:

Explicație pas cu pas:

$3^{23}\cdot 4^{23} - 2^{21}\cdot6^{23} = 3^{23}\cdot (2^2)^{23} - 2^{21}\cdot(2\cdot3)^{23} = 3^{23}\cdot 2^{2\cdot23} - 2^{21}\cdot2^{23}\cdot3^{23} =\\\\=3^{23}\cdot 2^{46} - 2^{21+23}\cdot3^{23} =3^{23}\cdot 2^{2+44} - 2^{44}\cdot3^{23} = 3^{23}\cdot2^2\cdot 2^{44}} - 2^{44}\cdot3^{23}=\\\\= 2^{44}\cdot3^{23}( 2^{2} -1) = 2^{44}\cdot3^{23}( 4} -1) =2^{44}\cdot3^{23}\cdot 3= 2^{44}\cdot3^{24} =2^{22\cdot2}\cdot3^{12\cdot2} = \\\\=(2^{22})^2}\cdot(3^{12})^2 = (2^{22}\cdot3^{12})^2$

Este patrat perfect