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If `a, b, c `are positive real numbers such that `ab^2c^3= 64` then minimum value of `1/a+2/b+3/c` is equal to

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Given `ab^2c^3=64` now we have to find minimum value of `1/a+2/b+3/c`.
this can be done by the concept fo` AM>=GM`, where AM and GM are the arithmetic and geometric mean.
Let there be 6 terms that are`1/a,1/b,1/b,1/c,1/c,1/c`, applying `AM>=GM` on them. we get,
`(1/a+2/b+3/c)/6>=(1/(ab^2c^3))^(1/6)`
`(1/a+2/b+3/c)/6>=3`
hence minimum value is 3.
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