Question

Không dùng máy tính , tính: P = \(\frac{2006}{2007}+\sqrt{1+2006^2+\frac{2006^2}{2007^2}}\)

Answer 1

\(P=\frac{2006}{2007}+\sqrt{1+2006^2+\frac{2006^2}{2007^2}}\)

ta có : \(\left(1+2006\right)^2=2006^2+1+2.2006\)

\(\Leftrightarrow2006^2+1=2007^2-2.2006\)

=> P = \(\frac{2006}{2007}\) + \(\sqrt{2007^2-2.2006+\frac{2006^2}{2007^2}}\)

= \(\frac{2006}{2007}+\sqrt{\left(2007-\frac{2006}{2007}\right)^2}\)

= \(\frac{2006}{2007}+\left|2007-\frac{2006}{2007}\right|\)

= \(\frac{2006}{2007}+2007-\frac{2006}{2007}=2007\)