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Find all positive real solutions to `4x+(18)/(y)=14,2y+(9)/(z)=15,9z+(16)/(x)=17`.

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Adding all the given equation, we have
`4x + (16)/(x) + 2y + (18)/(y) + 9z + (9)/(0) = 46`
Now, using A.M `ge` G.M we have
`4x + (16)/(x) ge 16, 2y + (18)/(y) 12` and `9z + (9)/(z) 18`
`:. 4x + (16)/(x) + 2y + (18)/(y) + 9z + (9)/(z) ge 46`
So, equation (1) holds only if `4x + (16)/(x) = 16, 2y, + (18)/(y) =12` and
`9z + (9)/(z) = 18`
`:. 4x = (16)/(x), 2y = (18)/(y)` and `9z = (9)/(z)`
`:. x = 2, y = 3` and `z = 1`
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