Question

So sánh x và y biết : \(x=\frac{2016^{2017}+1}{2016^{2016}+1}\) và \(y=\frac{2016^{2016}+1}{2016^{2015}+1}\)

Answer 1

Ta có :

\(x=\frac{2016^{2017}+1}{2016^{2016}+1}\)

\(\frac{1}{2016}x=\frac{2016^{2017}+1}{2016^{2017}+2016}=\frac{2016^{2017}+2016-2015}{2016^{2017}+2016}\)

\(\Rightarrow\frac{1}{2006}x=1-\frac{2015}{2016^{2017}+2016}\)

Ta lại có :

\(y=\frac{2016^{2016}+1}{2016^{2015}+1}\)

\(\Rightarrow\frac{1}{2016}y=\frac{2016^{2016}+1}{2016^{2016}+2016}=\frac{2016^{2016}+2016-2015}{2016^{2016}+2016}\)

\(\Rightarrow\frac{1}{2016}y=1-\frac{2015}{2016^{2016}+2016}\)

Mà \(\frac{2015}{2016^{2017}+2016}< \frac{2015}{2016^{2016}+2016}\)(so sánh mẫu)

\(\Rightarrow1-\frac{2015}{2016^{2017}+2016}>1-\frac{2015}{2016^{2016}+2016}\)

\(\Rightarrow\frac{1}{2016}x>\frac{1}{2016}y\)

\(\Rightarrow x>y\)

Answer 2

DÀI QUÁ KHÔNG TÍNH ĐƯỢC. CÁI NÀY CÓ MÀ ĐI HỎI THẦN ĐỒNG VỀ MÔN TOÁN ĐI

Answer 3

\(x< \frac{2016^{2017}+1+2015}{2016^{2016}+1+2015}\)

\(\Rightarrow x< \frac{2016^{2017}+2016}{2016^{2016}+2016}\)

\(\Rightarrow x< \frac{2016.\left(2016^{2016}+1\right)}{2016.\left(2016^{2015}+1\right)}\)

\(\Rightarrow x< y\)

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