Question Number 149891 by mathdanisur last updated on 08/Aug/21

if x;y;z;m;n;p∈R^+ then prove that: Σ_(cyc) ((m(x+y))/( (√((n+2p)x^2 +2nxy+(n+2p)y^2 )))) ≤ ((3m)/( (√(n+p))))

Answered by dumitrel last updated on 08/Aug/21

Σ((m(x+y))/( (√(n(x+y)^2 +2p(x^2 +y^2 )))))≤Σ((m(x+y))/( (√(n(x+y)^2 +2p(((x+y)^2 )/2))))) =Σ((m(x+y))/( (√((n+p)(x+y)^2 ))))=Σ(m/( (√(n+p))))=((3m)/( (√(n+p))))

Commented bymathdanisur last updated on 08/Aug/21

Cool Ser, thank you