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a: 200<314
=>1/200>1/314
=>17/200>17/314
b: 11/54=22/108
37<108
=>22/37>22/108
=>22/37>11/54
c: 141/893=3/19
159/901=3/17
mà 3/19<3/17
nên 141/893<159/901
d: 9/382=18/764=90/3820
6/257=18/771=90/3855
15/643=90/3858
3820<3855<3858
=>90/3820>90/3855>90/3858
=>9/382>6/257>15/643
a: 200<314
=>1/200>1/314
=>17/200>17/314
b: 11/54=22/108
37<108
=>22/37>22/108
=>22/37>11/54
c: 141/893=3/19
159/901=3/17
mà 3/19<3/17
nên 141/893<159/901
d: 9/382=18/764=90/3820
6/257=18/771=90/3855
15/643=90/3858
3820<3855<3858
=>90/3820>90/3855>90/3858
=>9/382>6/257>15/643
Ta có:
x = \(\frac{17^{16}-3}{17^{16}+1}=\frac{17^{16}+1-4}{17^{16}+1}=\frac{17^{16}+1}{17^{16}+1}-\frac{4}{17^{16}+1}=1-\frac{4}{17^{16}+1}\)
y = \(\frac{17^{17}-3}{17^{17}+1}=\frac{17^{17}+1-4}{17^{17}+1}=\frac{17^{17}+1}{17^{17}+1}-\frac{4}{17^{17}+1}=1-\frac{4}{17^{17}+1}\)
Do \(\frac{4}{17^{16}+1}>\frac{4}{17^{17}+1}\) => \(-\frac{4}{17^{16}+1}< -\frac{4}{17^{17}+1}\) => \(1-\frac{4}{17^{16}+1}< 1-\frac{4}{17^{17}+1}\)
=> x < y
\(\frac{x+2}{7}=\frac{y-3}{5}=\frac{z}{3}=\frac{x+2+y-3-z}{7+5-3}=\frac{x+y-z-1}{9}=\frac{-17-1}{9}=\frac{-18}{9}=-2\)
\(\frac{x+2}{7}=-2\Rightarrow x=-16\)
\(\frac{y-3}{5}=-2\Rightarrow y=-12\)
\(\frac{z}{3}=-2\Rightarrow z=-6\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\dfrac{x+2}{7}=\dfrac{y-3}{5}=\dfrac{z}{3}=\dfrac{x+2+y-3-z}{7+5-3}=\dfrac{-17-1}{9}=-\dfrac{18}{9}=-2\)\(\Rightarrow\left\{{}\begin{matrix}x=-2.7-2=-16\\y=-2.5+3=-13\\z=-2.3=-6\end{matrix}\right.\)