Question

Tính A=\(\sqrt{1+2016^2+\frac{2016^2}{2017^2}}+\frac{2016}{2017}\)

Answer 1

\(A=\sqrt{2016^2+\frac{2017}{2017}+\frac{2016^2-1}{2017^2}-\frac{1}{2017^2}}+\frac{2016}{2017}\)

\(A=\sqrt{2016^2+\frac{1}{2017^2}+\frac{2015.2017}{2017^2}+\frac{2017}{2017}}+\frac{2016}{2017}\)

\(A=\sqrt{2016^2+2.2016.\frac{1}{2017}+\frac{1^2}{2017^2}}+\frac{2016}{2017}\)

\(A=\sqrt{\left(2016+\frac{1}{2017}\right)^2}+\frac{2016}{2017}\)

\(A=\left(2016+\frac{1}{2017}\right)+\frac{2016}{2017}\)

A = 2017

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