Question

Arătați că nr:3²³×4²³-2²¹×6²³​ este pătrat perfect​

Answer 1

Răspuns: Ai demonstratia mai jos

Explicație pas cu pas:

Salutare!

$\bf 3^{23}\cdot 4^{23}-2^{21}\cdot 6^{23} =$

$\bf 3^{23}\cdot (2^{2})^{23}-2^{21}\cdot 2^{23}\cdot 3^{23} =$

$\bf 3^{23}\cdot 2^{2\cdot23}-2^{21}\cdot 2^{23}\cdot 3^{23} =$

$\bf 3^{23}\cdot 2^{46}-2^{21}\cdot 2^{23}\cdot 3^{23} =$

$\bf 2^{23}\cdot 3^{23}\cdot(3^{23-23}\cdot 2^{46-23}-2^{21}\cdot 2^{23-23}\cdot 3^{23-23}) =$

$\bf 2^{23}\cdot 3^{23}\cdot(3^{0}\cdot 2^{23}-2^{21}\cdot 2^{0}\cdot 3^{0}) =$

$\bf 2^{23}\cdot 3^{23}\cdot(1\cdot 2^{23}-2^{21}\cdot 1\cdot 1) =$

$\bf 2^{23}\cdot 3^{23}\cdot( 2^{23}-2^{21}) =$

$\bf 2^{23}\cdot 3^{23}\cdot 2^{21}\cdot ( 2^{23-21}-2^{21-21}) =$

$\bf 2^{23+21}\cdot 3^{23}\cdot ( 2^{2}-2^{0}) =$

$\bf 2^{44}\cdot 3^{23}\cdot ( 4-1) =$

$\bf 2^{44}\cdot 3^{23}\cdot 3 =$

$\bf 2^{44}\cdot 3^{23+1}=$

$\bf 2^{44}\cdot 3^{24}=$

$\bf (2^{22}\cdot 3^{12})^{2} \implies patrat\: perfect$

==pav38==