Question Number 148364 by mathdanisur last updated on 27/Jul/21

Commented bydumitrel last updated on 27/Jul/21

⇔(ae^(x/2) +be^(y/2) )^2 ≥e^((ax+by)/(a+b)) ⇔ ae^(x/2) +be^(y/2) ≥e^((ax+by)/(2(a+b))) f(x)=e^(x/2) convexa;(a/(a+b))+(b/(a+b))=1⇒ (a/(a+b))e^(x/2) +(b/(a+b))e^(y/2) ≥c^((a/(a+b))∙(x/2)+(b/(a+b))∙(y/2)) =e^((ax+by)/(2(a+b)))

Commented bymathdanisur last updated on 27/Jul/21

Thank you Ser