Numere
Posted: Mon Apr 20, 2009 6:11 pm
Aratati ca daca \( a,b,c \in R \) si \( (a+b+c)^3=a^3+b^3+c^3 \), atunci:
\( (a+b+c)^{2003} =a^{2003} +b^{2003} +c^{2003} \)
\( (a+b+c)^{2003} =a^{2003} +b^{2003} +c^{2003} \)
stim ca
\( 0=(a+b+c)^3-(a^3+b^3+c^3)=3(a+b)(b+c)(a+c) \)
WLOG presupunem \( a+b=0 \)
\( a=-b \)
De unde iese imediat relatia ceruta.