$$\dfrac{a}{b} + \dfrac{b}{a} = \dfrac{a^2+b^2}{ab} \implies a^2 + b^2 = 3ab \implies (a+b)^2 = 5ab$$$$\dfrac{a^2 + b^2}{2(a+b)^2} = \dfrac{3ab}{10ab} \implies \boxed{\dfrac{a^2 + b^2}{2(a+b)^2} = 0,3}$$$$\bf{Alternativa~(B)}$$