$\displaystyle please\,\, have \,\,a \,\,try !$
$\displaystyle (1) a+b+c=1$
$\displaystyle (2)a,b,c \in R^+$
$\displaystyle prove :\,\,27(a^3+b^3+c^3)\geq 6(a^2+b^2+c^2)+1 $
$\displaystyle with \,\,greatest \,\, appreciation \,\,! !$
$\displaystyle please\,\, have \,\,a \,\,try !$
$\displaystyle (1) a+b+c=1$
$\displaystyle (2)a,b,c \in R^+$
$\displaystyle prove :\,\,27(a^3+b^3+c^3)\geq 6(a^2+b^2+c^2)+1 $
$\displaystyle with \,\,greatest \,\, appreciation \,\,! !$