设实数a,b,c,满足a^2+2b^2+3c^2=3/2,求1/2^a+1/4^b+1/8^c的最小值
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![设实数a,b,c,满足a^2+2b^2+3c^2=3/2,求1/2^a+1/4^b+1/8^c的最小值](/uploads/image/z/5007123-27-3.jpg?t=%E8%AE%BE%E5%AE%9E%E6%95%B0a%2Cb%2Cc%2C%E6%BB%A1%E8%B6%B3a%5E2%2B2b%5E2%2B3c%5E2%3D3%2F2%2C%E6%B1%821%2F2%5Ea%2B1%2F4%5Eb%2B1%2F8%5Ec%E7%9A%84%E6%9C%80%E5%B0%8F%E5%80%BC)
设实数a,b,c,满足a^2+2b^2+3c^2=3/2,求1/2^a+1/4^b+1/8^c的最小值
设实数a,b,c,满足a^2+2b^2+3c^2=3/2,求1/2^a+1/4^b+1/8^c的最小值
设实数a,b,c,满足a^2+2b^2+3c^2=3/2,求1/2^a+1/4^b+1/8^c的最小值
(1/2)^a+(1/4)^b+(1/8)^c
=(1/2)^a+(1/2)^2b+(1/2)^3c
≥3[(1/2)^a•(1/2)^2b•(1/2)^3c]^(1/3)
=3[(1/2)^(a+2b+3c)]^(1/3)
=3(1/2)^(1/2)=3√2/2
即最小值为3√2/2