Question

Tính giá trị biểu thức:

P= \(|a-\dfrac{1}{2014}|+|a-\dfrac{1}{2016}|\) , với a = \(\dfrac{1}{2015}\)

Answer 1

Thay a=\(\dfrac{1}{2015}\) vào P, ta có:

\(P=\left|\dfrac{1}{2015}-\dfrac{1}{2014}\right|+\left|\dfrac{1}{2015}-\dfrac{1}{2016}\right|\) (*)

Vì \(\left\{{}\begin{matrix}\dfrac{1}{2015}< \dfrac{1}{2014}\\\dfrac{1}{2015}>\dfrac{1}{2016}\end{matrix}\right.\) nên (*) \(\Rightarrow P=\dfrac{1}{2014}-\dfrac{1}{2015}+\dfrac{1}{2015}-\dfrac{1}{2016}=\dfrac{1}{2030112}\)

Vậy ...

Answer 2

\(P=\left|a-\dfrac{1}{2014}\right|+\left|a-\dfrac{1}{2016}\right|\\ =\left|\dfrac{1}{2014}-a\right|+\left|a-\dfrac{1}{2016}\right|\\ =\left|\dfrac{1}{2014}-\dfrac{1}{2015}\right|+\left|\dfrac{1}{2015}-\dfrac{1}{2016}\right|\\ =\dfrac{1}{2014}-\dfrac{1}{2015}+\dfrac{1}{2015}-\dfrac{1}{2016}\\ =\dfrac{1}{2014}-\dfrac{1}{2016}\\ =\dfrac{2}{2014\cdot2016}\\ =\dfrac{1}{2030112}\)