已知正实数u,v,w,满足u^2+v^2+w^2=8,求u^4/9+v^4/16+w^4/25的最小值

已知正实数u,v,w,满足u^2+v^2+w^2=8,求u^4/9+v^4/16+w^4/25的最小值
已知正实数u,v,w,满足u^2+v^2+w^2=8,求u^4/9+v^4/16+w^4/25的最小值

已知正实数u,v,w,满足u^2+v^2+w^2=8,求u^4/9+v^4/16+w^4/25的最小值
权方和不等式有
(u^2)^2/9 + (v^2)^2/16+(w^2)^2/25 >= (u^2+v^2+w^2)^2 / (9+16+25) = 8^2/50 = 64/50 = 32/25