Question

Tính: \(\sqrt{1+2013^2+\dfrac{2013^2}{2014^2}}+\dfrac{2013}{2014}\)

Giúp em các anh chị oi

Answer 1

Đặt biểu thức trên là A

Ta có:

\(A=\sqrt{\dfrac{2014^2+2013^2.2014^2+2013^2}{2014^2}}+\dfrac{2013}{2014}\)

\(=\dfrac{\sqrt{2014^2-2.2013.2014+2013^2+2013^2.2014^2+2.2013.2014}}{2014}+\dfrac{2013}{2014}\)

\(=\dfrac{\sqrt{1+2.2013.2014+\left(2013.2014\right)^2}}{2014}+\dfrac{2013}{2014}\)

\(=\dfrac{\sqrt{\left(2013.2014+1\right)^2}}{2014}+\dfrac{2013}{2014}\)\(=\dfrac{2013.2014+1+2013}{2014}\)\(=2014\)