1AM≥GM
(a2009+b2009+c2009)/3 ≥ (abc) (2009/3)
1≥(abc) (2009/3)
abc ≤ 1
so (abc)4/3 ≤ 1 ----(1)
now applying AM≥GM again
(a4+b4+c4)/3 ≥ (abc)4/3 -----(2)
From (1) and (2) :
(a4+b4+c4) ≥ 3
Ans. 3
$\textbf{If $\mathbf{a,b,c>0}$ and $\mathbf{a^{2009}+b^{2009}+c^{2009}=3}.$ Then Find Max. and\\\\ Min. value of $\mathbf{a^4+b^4+c^4}$}
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