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\(\frac{x}{19}=\frac{19^{17}+1}{19^{17}+19}=1-\frac{18}{19^{17}+19}\)
\(\frac{y}{19}=\frac{19^{16}+1}{19^{16}+19}=1-\frac{18}{19^{16}+19}\)
Nhận thấy 1917 + 19 > 1916 + 19
=> \(\frac{18}{19^{17}+19}< \frac{18}{19^{16}+19}\)
=> \(-\frac{18}{19^{17}+19}>-\frac{18}{19^{16}+19}\)
=> \(1-\frac{18}{19^{17}+19}>1-\frac{18}{19^{16}+19}\)
=> \(\frac{x}{19}>\frac{y}{19}\)
=> x > y
Vậy x > y
Ta có : \(\frac{x}{19}=\frac{19^{17}+1}{19^{17}+19}=1-\frac{18}{19^{17}+19}\)
\(\frac{y}{19}=\frac{19^{16}+1}{19^{16}+19}=1-\frac{18}{19^{16}+19}\)
Vì\(\frac{18}{19^{17}+19}< \frac{18}{19^{16}+19}\)\(\Rightarrow\frac{x}{19}>\frac{y}{19}\)
mà \(x,y>0\)
\(\Rightarrow x>y\)
Trả lời:
\(x=\frac{9^{11}+2}{9^{11}+3}=\frac{9^{11}+3-1}{9^{11}+3}=\frac{9^{11}+3}{9^{11}+3}-\frac{1}{9^{11}+3}=1-\frac{1}{9^{11}+3}\)
\(y=\frac{9^{12}+2}{9^{12}+3}=\frac{9^{12}+3-1}{9^{12}+3}=\frac{9^{12}+3}{9^{12}+3}-\frac{1}{9^{12}+3}=1-\frac{1}{9^{12}+3}\)
Ta có: \(9^{11}< 9^{12}\)
\(\Leftrightarrow9^{11}+3< 9^{12}+3\)
\(\Leftrightarrow\frac{1}{9^{11}+3}>\frac{1}{9^{12}+3}\)
\(\Leftrightarrow-\frac{1}{9^{11}+3}< -\frac{1}{9^{12}+3}\)
\(\Leftrightarrow1-\frac{1}{9^{11}+3}< 1-\frac{1}{9^{12}+3}\)
\(\Leftrightarrow x< y\)
Vậy x < y
Ta có: 9/16=27/48
: -13/-24=13/24=26/48
Mà:27>26=>27/48>26/48
Nên 9/16>-13/-24
Ta có: x = \(\frac{7^{16}-3}{7^{16}+1}=\frac{7^{16}+1-4}{7^{16}+1}=1-\frac{4}{7^{16}+1}\)
y = \(\frac{7^{17}-3}{7^{17}+1}=\frac{7^{17}+1-4}{7^{17}+1}=1-\frac{4}{7^{17}+1}\)
Do \(7^{16}+1< 7^{17}+1\) => \(\frac{4}{7^{16}+1}>\frac{4}{7^{17}+1}\) => \(-\frac{4}{7^{16}+1}< -\frac{4}{7^{17}+1}\)
=> \(1-\frac{4}{7^{16}+1}< 1-\frac{4}{7^{17}+1}\) => x < y
Trả lời:
\(x=\frac{7^{16}-3}{7^{16}+1}=\frac{7^{16}+1-4}{7^{16}+1}=\frac{7^{16}+1}{7^{16}+1}-\frac{4}{7^{16}+1}=1-\frac{4}{7^{16}+1}\)
\(y=\frac{7^{17}-3}{7^{17}+1}=\frac{7^{17}+1-4}{7^{17}+1}=\frac{7^{17}+1}{7^{17}+1}-\frac{4}{7^{17}+1}=1-\frac{4}{7^{17}+1}\)
Ta có: \(7^{16}< 7^{17}\)
\(\Leftrightarrow7^{16}+1< 7^{17}+1\)
\(\Leftrightarrow\frac{4}{7^{16}+1}>\frac{4}{7^{17}+1}\)
\(\Leftrightarrow-\frac{4}{7^{16}+1}< -\frac{4}{7^{17}+1}\)
\(\Leftrightarrow1-\frac{4}{7^{16}+1}< 1-\frac{4}{7^{17}+1}\)
\(\Leftrightarrow x< y\)
Vậy x < y
Ta có \(\hept{\begin{cases}\left|x-y+2\right|\ge0\forall x;y\\\left|2y+1\right|\ge0\forall x;y\end{cases}}\Leftrightarrow\left|x-y+2\right|+\left|2y+1\right|\ge0\forall x;y\)
Kết hợp đề bài
=> \(\left|x-y+2\right|+\left|2y+1\right|=0\)
=> \(\hept{\begin{cases}x-y+2=0\\2y+1=0\end{cases}}\Leftrightarrow\hept{\begin{cases}x=-\frac{5}{2}\\x=-\frac{1}{2}\end{cases}}\)
Vậy x = -5/2 ; y = -1/2
Ta có 13x = \(\frac{13^{17}+13}{13^{17}+1}=1+\frac{12}{13^{17}+1}\)
13y = \(\frac{13^{16}+13}{13^{16}+1}=1+\frac{12}{13^{16}+1}\)
Vì 1317 + 1 > 1316 + 1
=> \(\frac{1}{13^{17}+1}< \frac{1}{13^{16}+1}\)
=> \(\frac{12}{13^{17}+1}< \frac{12}{13^{16}+1}\)
=> \(1+\frac{12}{13^{17}+1}< 1+\frac{12}{13^{16}+1}\)
=> 13x < 13y
=> x < y
Vậy x < y