Răspuns: Ai demonstratia mai jos
Explicație pas cu pas:
Salutare!
[tex]\bf 3^{23}\cdot 4^{23}-2^{21}\cdot 6^{23} =[/tex]
[tex]\bf 3^{23}\cdot (2^{2})^{23}-2^{21}\cdot 2^{23}\cdot 3^{23} =[/tex]
[tex]\bf 3^{23}\cdot 2^{2\cdot23}-2^{21}\cdot 2^{23}\cdot 3^{23} =[/tex]
[tex]\bf 3^{23}\cdot 2^{46}-2^{21}\cdot 2^{23}\cdot 3^{23} =[/tex]
[tex]\bf 2^{23}\cdot 3^{23}\cdot(3^{23-23}\cdot 2^{46-23}-2^{21}\cdot 2^{23-23}\cdot 3^{23-23}) =[/tex]
[tex]\bf 2^{23}\cdot 3^{23}\cdot(3^{0}\cdot 2^{23}-2^{21}\cdot 2^{0}\cdot 3^{0}) =[/tex]
[tex]\bf 2^{23}\cdot 3^{23}\cdot(1\cdot 2^{23}-2^{21}\cdot 1\cdot 1) =[/tex]
[tex]\bf 2^{23}\cdot 3^{23}\cdot( 2^{23}-2^{21}) =[/tex]
[tex]\bf 2^{23}\cdot 3^{23}\cdot 2^{21}\cdot ( 2^{23-21}-2^{21-21}) =[/tex]
[tex]\bf 2^{23+21}\cdot 3^{23}\cdot ( 2^{2}-2^{0}) =[/tex]
[tex]\bf 2^{44}\cdot 3^{23}\cdot ( 4-1) =[/tex]
[tex]\bf 2^{44}\cdot 3^{23}\cdot 3 =[/tex]
[tex]\bf 2^{44}\cdot 3^{23+1}=[/tex]
[tex]\bf 2^{44}\cdot 3^{24}=[/tex]
[tex]\bf (2^{22}\cdot 3^{12})^{2} \implies patrat\: perfect[/tex]
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