Sum the means of the two integers
Haskell, 48 bytes



a%b=sum[((a**p+b**p)/2)**(1/p)|p&lt;-[2,1,-1,1e-9]]


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This uses the fact that the root-square, arithmetic, harmonic, and geometric means are all special cases of the generalized mean ((a**p+b**p)/2)**(1/p) for p=2,1,-1,0. The geometric mean uses the limit p-&gt;0+, approximated as p=1e-9 which suffices for precision.