+) \(2004^{10}+2004^9\)

\(=2004^9\left(2004+1\right)=2004^9.2005\)

+) \(2005^{10}=2005^9.2005\)

Mà \(2005^9>2004^9\)

\(\Rightarrow2004^{10}+2004^9< 2005^{10}\)

${2004}^{10}+{2004}^9={2004}^9\left(2004+1\right)$
$={2004}^9.2005<{2005}^9.2005={2005}^{10}$
Nên ${2004}^{10}+{2004}^9<{2005}^{10}$

0,2 . x - 75 : 2,5 = 6,08 : 0,04

<=> 0,2x - 30 = 152

<=> 0,2x = 182

<=> x = 910

0,2 x x - 75 : 2,5 = 6,08 : 0,04

0,2 x x - 50 = 152

0,2 x x = 152 + 50

0,2 x x = 202

x = 202 : 0,2

x = 1010

4/9 x X + 14/9 x X = 13,2 : 0,01

= 4/9 x X + 14/9 x X = 1320 

= X . ( 4/9 + 14/9) = 1320

= X . 2 = 1320

= X = 1320 : 2

= X = 660 

4/9 x X + 14/9 x X = 13,2 : 0,01

= 4/9 x X + 14/9 x X = 1320 

= X . ( 4/9 + 14/9) = 1320

= X . 2 = 1320

= X = 1320 : 2

= X = 660 

\(\left(x-1\right)\left(x-3\right)< 0\)

\(\Leftrightarrow\left\{{}\begin{matrix}x-1>0\\x-3< 0\end{matrix}\right.\) hoặc \(\left\{{}\begin{matrix}x-1< 0\\x-3>0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x>1\\x< 3\end{matrix}\right.\) hoặc \(\left\{{}\begin{matrix}x< 1\\x>3\end{matrix}\right.\)( vô lí ) 

\(\Leftrightarrow1< x< 3\)

\(A< 0\)

\(\Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x-1>0\\x-3< 0\end{matrix}\right.\left(TM\right)}\\\left\{{}\begin{matrix}x-1< 0\\x-3>0\end{matrix}\right.\left(L\right)}\end{matrix}\right.\Rightarrow1< x< 3}\)

480 ⋮ a ⇔ a ϵ Ư(480) 

Ư(480) = {1; 2; 3;4;5; 6;8;10;12;15;16;20;24;30;32;40;60;96;160;480}

180 ⋮ x và 2 < x < 5

x ϵ Ư(180) 

Ư(180)  = {1;2;3;4;5;....180}

vì 2<x<5 ⇔ x = 3; 4

tìm cả a và x à bn

2n + 1⋮3n + 1

=> 3 (2n + 1)⋮3n + 1

=> 6n + 3⋮3n + 1

=> 2 (3n + 1) + 1⋮ 3n + 1

Vì 2(3n + 1) + 1⋮3n + 1 mà 2(3n + 1)⋮3n + 1 nên 1⋮3n + 1

=> 3n + 1ϵ Ư(1) = {1;-1}

=> n = 0

Vậy n = 0

   {132 - [ 115 - ( 16- 8) ] : 2} .5

= {132  -[ 115 - 8] :2} .5

= {132 - 107:2} .5

= \(\dfrac{157}{2}\) . 5

= 785/2

36 : { 336 : [ 200 - (12 + 8 : 20)]}

= 36: { 336 : [ 200 - 62/5]}

= 36 : { 336 : 938/5)

= 36 : 120/67

= 201/10

55 - [ 49 - ( 2³ .17 -2³ .14)]

= 55 - [ 49 -2³ ( 17-14)]

= 55 - [ 49 - 8.3}

= 55 - [ 49 - 24]

= 55 - 25

= 30

 {132 - [ 115 - ( 16- 8) ] : 2} .5

= {132  -[ 115 - 8] :2} .5

= {132 - 107:2} .5

= \dfrac{157}{2}2157​ . 5

= 785/2

36 : { 336 : [ 200 - (12 + 8 : 20)]}

= 36: { 336 : [ 200 - 62/5]}

= 36 : { 336 : 938/5)

= 36 : 120/67

= 201/10

55 - [ 49 - ( 23 .17 -23 .14)]

= 55 - [ 49 -23 ( 17-14)]

= 55 - [ 49 - 8.3}

= 55 - [ 49 - 24]

= 55 - 25

= 30

`3,5 : (x+1)-5,7=1,3`

`3,5 : (x+1)=1,3+5,7`

`3,5 : (x+1)=7`

`x+1=3,5:7`

`x+1=0,5`

`x=0,5-1`

`x=-0,5`

Vậy `x=-0,5`

\(3,5:\left(x+1\right)-5,7=1,3\)

\(\Leftrightarrow3,5:\left(x+1\right)=7\)

\(\Leftrightarrow x+1=\dfrac{1}{2}\)

\(\Leftrightarrow x=-\dfrac{1}{2}\)