If `x ,y ,z` are distinct positive numbers, then prove that `(x+y)(y+z)(z+x)>8x y zdot`

Explanation

We know that, `A.M>=G.M` for positive numbers we get,


Using `A.M>=G.M` on `x,y,` we get,


`(x+y)/2> sqrt(xy)`


`=> (x+y)>2sqrt(xy)`


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