Question

срочноооо!помогитееее,даю 20 баллов​

Answer 1

$\Big(\dfrac{a^2}{2}-\dfrac{a}{\sqrt2}+1\Big)\cdot \Big(\dfrac{a^2}{2}+\dfrac{a}{2}+1\Big)\cdot \dfrac{\sqrt2}{a^4+2a^2+4}=\\\\\\=\Big(\dfrac{a^2}{2}-\dfrac{\sqrt2a}{2}+\dfrac{2}{2}\Big)\cdot \Big(\dfrac{a^2}{2}+\dfrac{\sqrt2a}{2}+\dfrac{2}{2} \Big)\cdot \dfrac{\sqrt2}{a^4+2a^2+4}=\\\\\\=\dfrac{(a^2-\sqrt2a+2)(a^2+\sqrt2a+2)}{4}\cdot \dfrac{\sqrt2}{a^4+2a^2+4}=\\\\\\=\dfrac{(a^2+2)^2-(\sqrt2a)^2}{4}\cdot \dfrac{\sqrt2}{a^4+2a^2+4}=\dfrac{a^4+4a^2+4-2a^2}{4}\cdot \dfrac{\sqrt2}{(a^2+2)^2}=$

$=\dfrac{a^4+2a^2+4}{4}\cdot \dfrac{\sqrt2}{a^4+2a^2+4}=\dfrac{\sqrt2}{4}$