There are quite a few means in mathematics, such as the arithmetic mean, the geometric mean, and many others...
Definitions and Task
Note that these are the definitions for two positive integers*:
The root mean square is the square root of the sum of their squares halved ().
The arithmetic mean is their sum, halved ().
The geometric mean is the square root of their product ().
The harmonic mean is 2 divided by the sum of their inverses ( = ).
Given two integers a and b such that a, b ∈ [1, +∞), sum the means mentioned above of a and b. Your answers must be accurate to at least 3 decimal places, but you do not have to worry about rounding or floating-point precision errors.
a, b -> Output 7, 6 -> 25.961481565148972 10, 10 -> 40 23, 1 -> 34.99131878607909 2, 4 -> 11.657371451581236 345, 192 -> 1051.7606599443843
* There are many other means, but for the purposes of this challenge we'll use the ones mentioned in the "Definitions" section.