73 . 25 + 28 . 25 - 25
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a, 249 - 25 × 8 + 32 × 4
= 249 - 200 + 9 × 4
= 49 + 36
= 85
b,27 : { 480 : [(513 : 9 + 19 ) + 84 ]}
= 27 : { 480 : [(57 + 19) + 84 ]}
= 27 : { 480 : [76 + 84]}
= 27 : { 480 : 160}
= 27 : 3
= 9
c. 73 × 25 + 28 × 25 - 25
= 73 × 25 + 28 × 25 - 25 × 1
= 25 × (73 + 28 - 1)
= 25 × 100
= 2500
d. 2× 9 × 50 - 890
= (2 × 50) × 9 - 1
= 100 × 9 - 1
= 900 - 1
= 899
a)\(249-25\cdot8+3^2\cdot4\)
\(=249-200+9\cdot4\)
\(=49+36=85\)
b)\(27:\left\{480:\left[\left(513:9+19\right)+84\right]\right\}\)
\(=27:\left\{480:\left[\left(57+19\right)+84\right]\right\}\)
\(=27:\left\{480:\left[76+84\right]\right\}\)
\(=27:\left\{480:160\right\}\)
\(=27:3=9\)
c)\(73\cdot25+28\cdot25-25\)
\(=73\cdot25+28\cdot25-25\cdot1\)
\(=\left(73+28-1\right)\cdot25\)
\(=100\cdot25=2500\)
d)\(2\cdot9\cdot50-89^0\)
\(=2\cdot9\cdot50-1\)
\(=900-1=899\)
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\(\begin{array}{*{20}{c}}{ + \begin{array}{*{20}{c}}{36}\\{36}\end{array}}\\\hline{\,\,\,\,72}\end{array}\) \(\begin{array}{*{20}{c}}{ + \begin{array}{*{20}{c}}{73}\\{17}\end{array}}\\\hline{\,\,\,90}\end{array}\)
\(\begin{array}{*{20}{c}}{ + \begin{array}{*{20}{c}}{28}\\{53}\end{array}}\\\hline{\,\,\,81}\end{array}\) \(\begin{array}{*{20}{c}}{ + \begin{array}{*{20}{c}}{25}\\{35}\end{array}}\\\hline{\,\,\,60}\end{array}\)
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\(10,\Rightarrow x-14=-8\Rightarrow x=6\\ 11,\Rightarrow7-x-32=-25\\ \Rightarrow-25-x=-25\Rightarrow x=0\\ 12,\Rightarrow3x-16=\dfrac{2\cdot7^4}{7^3}=2\cdot7=14\\ \Rightarrow3x=30\Rightarrow x=10\\ 13,\Rightarrow\left[{}\begin{matrix}x-4=5\\x-4=-5\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=9\\x=-1\end{matrix}\right.\\ 14,\Rightarrow\left(2x+11\right)^2=2^4:2^4=1\\ \Rightarrow\left[{}\begin{matrix}2x+11=1\\2x+11=-1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-5\\x=-6\end{matrix}\right.\\ 15,\Rightarrow7^{3x-2}=7^3\cdot4+7^3\cdot3=7^3\cdot7=7^4\\ \Rightarrow3x-2=4\\ \Rightarrow3x=6\Rightarrow x=2\)
10) x - [42 + (-28)] = -8
x - 14 = -8
x = -8 + 14 = 6
11) (7-x) - (25 +7) = -25
(7 -x) - 32 = -25
7 -x = -25 + 32 = 7
x = 7 -7 = 0
12) (3x - 24) . 73 = 2 . 74
(3x - 16) . 343 = 4802
3x - 16 = 4802 : 343= 14
3x = 14 + 16 = 30
x = 30 : 3 =10
13) (x - 4)2 = 25
⇒ 52 = 25
⇒ x - 4 = 5
⇒ x = 5 + 4 =9
14) 24(2x + 11)2 = 42
16(2x + 11)2 = 16
(2x + 11)2 = 16 : 16 = 1
⇒ 2x + 11 = 1
⇒ 2x = 11 + 1 = 12
⇒ x = 12 : 2 = 6
15) 73x-2 - 3.73 = 73 . 4
73x-2 - 1029 = 1372
73x-2 = 1372 + 1029 = 2401
⇒ 74 = 2401
⇒ 3x - 2 = 4
⇒ 3x = 4 + 2 = 6
⇒ x = 6 : 3 =2
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a ) 126 - 2x = 12 - ( -28 )
126 - 2x = 40
2x = 126 - 40
2x = 86
x = 86 : 2
x = 43
b ) 25 - 5( x + 1 ) = 30 - 125
25 - ( 5x + 5 ) = -95
25 - 5x - 5 = -95
20 - 5x = -95
5x = 20 - ( - 95 )
5x = 115
x = 115 : 5
x = 23
c ) I 3x - 1 I - 25 = 73
I 3x - 1 I = 73 + 25
I 3x - 1 I = 98
=> 3x - 1 = 98 hoặc 3x - 1 = -98
=> 3x = 98 + 1 hoặc 3x = -98 + 1
=> 3x = 99 hoặc 3x = -97
=> x = 99 : 3 hoặc x = -97 : 3
=> x = 33 hoặc x = -93/3
d ) 2( x + 2 ) - 6 = 120 - 4x
2x + 4 - 6 = 120 - 4x
2x - 2 = 120 - 4x
2x + 4x = 120 + 2
6x = 122
x = 122 : 6
x = 61/3
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|25 - 24 -10| - (28 - 30 + 4)
= |1 - 10| - (-2 + 4)
= |-9| - 2
= 9 - 2
= 7
-(-73) + (44 - 94 + 27) + 94
= 73 + (-50 + 27) + 94
= 73 + (-23) + 94
= 73 - 23 + 94
= 50 + 94
= 144
(-33 + 108 - 75) - (108 + 25)
= (75 - 75) - 133
= 0 - 133
= -133
120 - (-2 + 120 - 18) - 92
= 120 - (118 - 18) - 92
= 120 - 100 - 92
= 20 - 92
= -72
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Lời giải:
Xét tử số:
$\text{TS}=1+25^4+25^8+...+25^{28}$
$25^4.\text{TS}=25^4+25^8+...+25^{32}$
$\Rightarrow \text{TS}(25^4-1)=25^{32}-1$
$\text{TS}=\frac{25^{32}-1}{25^4-1}$
Xét mẫu số:
$\text{MS}=1+25^2+..+25^{30}$
$25^2.\text{MS}=25^2+25^4+...+25^{32}$
$\Rightarrow \text{MS}(25^2-1)=25^{32}-1$
$\Rightarrow \text{MS}=\frac{25^{32}-1}{25^2-1}$
Do đó:
$A=\frac{25^{32}-1}{25^4-1}:\frac{25^{32}-1}{25^2-1}=\frac{25^2-1}{25^4-1}$
$=\frac{25^2-1}{(25^2-1)(25^2+1)}=\frac{1}{25^2+1}$
![](https://rs.olm.vn/images/avt/0.png?1311)
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73.25+28.25-25=25(73+28-1)=25.100=2500
=2500
k mình nha