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Ta có x=2015 => x+1 =2016.Thay vào biểu thức,ta có:
\(x^{10}-\left(x+1\right)x^9+\left(x+1\right)x^8-...+\left(x+1\right)x^2-\left(x+1\right)x+\left(x+1\right)\)
\(=x^{10}-x^{10}+x^9-x^9+...+x^2-x^2-x+x+1\)=1
(9/16)^2016.(16/9)^2015.4/3
9/16.(9/16)^2015.(16/9)^2015.4/3
9/16.(9/16.16/9)^2015.4/3
9/16.1^2015.4/3
9/16.1.4/3
=>9/16.4/3=3/4
\(\left(\dfrac{9}{16}\right)^{2016}.\left(\dfrac{16}{9}\right)^{2015}.\dfrac{4}{3}\)
\(=\left[\left(\dfrac{3}{4}\right)^2\right]^{2016}.\left[\left(\dfrac{4}{3}\right)^2\right]^{2015}.\dfrac{4}{3}\)
\(=\left(\dfrac{3}{4}\right)^{2018}.\left(\dfrac{4}{3}\right)^{2017}.\dfrac{4}{3}\)
\(=\left(\dfrac{3}{4}\right)^{2018}.\left(\dfrac{4}{3}\right)^{2018}\)
\(=\left(\dfrac{3}{4}.\dfrac{4}{3}\right)^{2018}\)
\(=\left(\dfrac{1}{1}.\dfrac{1}{1}\right)^{2018}\)
\(=1^{2018}\)
\(=1\)