Question

arata ca 100^2013 se poate scrie ca o suma de doua patrate perfecte

Answer 1

Răspuns:

Explicație pas cu pas:

100^2013=100*100^2012=(6^2+8^2)*[100^1006]^2=

6^2*[100^1006]^2+8^2*[100^1006]^2=[6*100^1006]^2+[8*100^1006]^2=

x^2+y^2 (suma de patrate perfecte)

Am folosit formulele:

a^(m*n)=[a^m]^n

a^m*b^m=(a*b)^m