Question 478747
1. {{{a^3+b^3=(a+b)(a^2-ab+b^2)}}}
if {{{a^3+b^3=0}}}, then {{{(a+b)(a^2-ab+b^3)=0}}}, so 
{{{a+b=0}}} or {{{a^2-ab+b^2=0}}}
2. If we have {{{log ((a+b)) -(1/2) * (log a+ log b+ log 3)}}} then {{{a+b}}} can not be equal 0 (domain of the function {{{log((a+b))}}} is {{{a+b>0}}}), so {{{a^2-ab+b^2}}} has to be equal 0
 {{{log ((a+b)) -(1/2) * (log a+ log b+ log 3)=(1/2)(2log (a+b) - (log a+ log b+ log 3))}}}
Use formula {{{n*loga=log(a^n)}}}, {{{loga+logb=log(ab)}}}, {{{loga-logb=log(a/b)}}}
{{{(1/2)(2log( (a+b)) - (log a+ log b+ log 3))=(1/2)(log( (a+b)^2)-log((3 ab)))=(1/2)log(((a^2+2ab+b^2)/(3ab)))=(1/2)log((((a^2-ab+b^2)+3ab)/(3ab)))=(1/2)log((0+(3ab)/(3ab)))=(1/2)log1=0}}}