`@` `\text {Ans}`

`\downarrow`

`315/380 = 1 - 65/380`

`316/380 = 1 - 65/381`

Mà `65/380 > 65/381`

`-> 1 - 65/380 < 1 - 65/381`

`-> 315/380 < 316/381`

`=> -315/380 > -316/381`

315/380=1-65/380

316/381=1-65/381

mà 65/380>65/381

nên 315/380<316/381

=>-315/380>-316/381

\(-\dfrac{249:3}{333:3}=-\dfrac{83}{111}\Rightarrow-\dfrac{249}{333}=-\dfrac{83}{111}\)

-315/380 = -120015/144780

-316/381 = -120080/144780

Do -120015 > -120080

-120015/144780 > -120080/144780

⇒ -315/380 > -316/381

387/-389 => -387/389     và -387/389> -389/391 nhé

(x-1)²⁰²⁰=(x-1)²⁰²²

=>(x-1)²⁰²⁰-(x-1)²⁰²²=0

=>(x-1)²⁰²⁰-(x-1)²⁰²⁰.(x-1)²=0

=>(x-1)²⁰²⁰(1-(x-1)²=0

=>(x-1)²⁰²⁰=0 hoặc 1-(x-1)²=0

=>x=1 hoặc x=2.

Bài 2

a,2¹⁰⁵ và 5⁴⁵

2¹⁰⁵=(2⁷)¹⁵=128¹⁵

5⁴⁵=(5³)¹⁵=125¹⁵

Vì 128^15_>12515 nên 2¹⁰⁵>5⁴⁵.

b,

5⁵⁴ và 3⁸¹

5⁵⁴=(5⁶)⁹=15625⁹

3⁸¹=(3⁹)⁹=19683⁹

Vì 15625⁹<19683⁹ nên 5⁵⁴<3⁸¹

Bài 1 :

\(\left(x-1\right)^{2020}=\left(x-1\right)^{2022}\)

\(\Rightarrow\left(x-1\right)^{2022}-\left(x-1\right)^{2020}=0\)

\(\Rightarrow\left(x-1\right)^{2020}\left[\left(x-1\right)^2-1\right]=0\)

\(\Rightarrow\left[{}\begin{matrix}x-1=0\\\left(x-1\right)^2-1=0\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=0\\\left(x-1\right)^2=1\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=0\\x-1=1\\x-1=-1\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=0\\x=2\\x=0\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=0\\x=2\end{matrix}\right.\)

Ta có : \(\frac{377}{399}=1-\frac{22}{399}\)

\(\frac{379}{381}=1-\frac{2}{381}\)

Vì \(\frac{22}{399}>\frac{2}{381}\)nên \(\frac{377}{399}< \frac{379}{381}\)

Vì 2016>2013.

=>\(\frac{387}{2016}< \frac{387}{2013}\left(1\right)\)

Vì 387>109.

=>\(\frac{387}{2016}>\frac{109}{2016}\left(2\right)\)

Từ (1) và (2),suy ra:

\(\frac{109}{2016}< \frac{387}{2013}\)

Vậy............

dấu < nha bạn tích mk với

\(\frac{109}{2016}\)và  \(\frac{387}{2013}\)

\(\frac{109}{2016}=\frac{109}{2016}+\frac{1907}{2016}\)       \(\frac{387}{2013}=\frac{387}{2013}+\frac{1626}{2013}\)

Ta thấy \(\frac{1907}{2016}>\frac{1626}{2013}\)

\(\Rightarrow\frac{109}{2016}>\frac{387}{2013}\)

a: \(0.2=\dfrac{2}{10}\)

10>7

=>\(\dfrac{2}{10}< \dfrac{2}{7}\)

=>\(\dfrac{2}{7}>0.2\)

b: \(-\dfrac{1^5}{6}=\dfrac{-1}{6}=\dfrac{-3}{18}\)

\(\dfrac{8}{-9}=-\dfrac{16}{18}\)

mà -3>-16

nên \(-\dfrac{1^5}{6}>\dfrac{8}{-9}\)

c: \(\dfrac{2017}{2016}>1\)

\(1>\dfrac{2017}{2018}\)

Do đó: \(\dfrac{2017}{2016}>\dfrac{2017}{2018}\)

d: \(-\dfrac{249}{333}=\dfrac{-249:3}{333:3}=\dfrac{-83}{111}\)

e: \(\dfrac{5^1}{3}=\dfrac{5}{3}=\dfrac{15}{9}\)

\(\dfrac{4^8}{9}=\dfrac{65536}{9}\)

mà 15<65536

nên \(\dfrac{5^1}{3}< \dfrac{4^8}{9}\)

f: 13,589<13,612