Question

mn giúp em câu 2) với ạ

Answer 1

Từ câu 1:

\(\Rightarrow a^2=\dfrac{\sqrt{2}}{4}\left(1-a\right)\Rightarrow a^4=\dfrac{1}{8}\left(a^2-2a+1\right)\)

\(\Rightarrow a^4+a+1=\dfrac{a^2-2a+1}{8}+a+1=\dfrac{\left(a+3\right)^2}{8}\)

\(\Rightarrow S=a^2+\sqrt{\dfrac{\left(a+3\right)^2}{8}}=a^2+\dfrac{a+3}{2\sqrt{2}}=\dfrac{\sqrt{2}}{4}\left(1-a\right)+\dfrac{\sqrt{2}}{4}\left(a+3\right)\)

\(=\dfrac{\sqrt{2}}{4}\left(1-a+a+3\right)=\sqrt{2}\)