a fost răspuns

Scrieti numarul 8 la 2014 ca diferenta a doua patrate perfecte.

Răspuns :

[tex]8^{2014} = 8^{2} 8^{2012} =(9-1) ^{2} ( 8^{1006} ) ^{2} = (3^{2} - 1^{2} )(8^{1006}) ^{2} [/tex][tex]= 3^{2} (8^{1006}) ^{2} - (8^{1006}) ^{2} = (3 8^{1006}) ^{2} - (8^{1006} ) ^{2} [/tex]
8^2014=8^2x8^2012=64x8^2012=(100-36)x8^2012=(10^2-6^2)x8^2012=
=10^2x8^2012-6^2x8^2012=(10x8^1006)^2-(6x8^1006)^2

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