22.(x-32)+4=20
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Bài 1
S₂ = 21 + 23 + 25 + ... + 1001
Số số hạng của S₂:
(1001 - 21) : 2 + 1 = 491
⇒ S₂ = (1001 + 21) . 491 : 2 = 250901
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S₄ = 15 + 25 + 35 + ... + 115
Số số hạng của S₄:
(115 - 15) : 10 + 1 = 11
⇒ S₄ = (115 + 15) . 11 : 2 = 715
Bài 2
a) 2x - 138 = 2³.3²
2x - 138 = 8.9
2x - 138 = 72
2x = 72 + 138
2x = 210
x = 210 : 2
x = 105
b) 5.(x + 35) = 515
x + 35 = 515 : 5
x + 35 = 103
x = 103 - 35
x = 78
c) 814 - (x - 305) = 712
x - 305 = 814 - 712
x - 305 = 102
x = 102 + 305
x = 407
d) 20 - [7.(x - 3) + 4] = 2
7(x - 3) + 4 = 20 - 2
7(x - 3) + 4 = 18
7(x - 3) = 18 - 4
7(x - 3) = 14
x - 3 = 14 : 7
x - 3 = 2
x = 2 + 3
x = 5
e) 9ˣ⁻¹ = 9
x - 1 = 1
x = 1 + 1
x = 2
\(A=\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+\dfrac{1}{3^4}+...+\dfrac{1}{3^{99}}\)
\(\Rightarrow\dfrac{A}{3}=\dfrac{1}{3^2}+\dfrac{1}{3^3}+\dfrac{1}{3^4}+...+\dfrac{1}{3^{100}}\)
\(\Rightarrow A-\dfrac{A}{3}=\dfrac{2A}{3}=\left(\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+...+\dfrac{1}{3^{99}}\right)-\left(\dfrac{1}{3^2}+\dfrac{1}{3^3}+\dfrac{1}{3^4}+...+\dfrac{1}{3^{100}}\right)\)
\(\Rightarrow\dfrac{2A}{3}=\left(\dfrac{1}{3^2}-\dfrac{1}{3^2}\right)+\left(\dfrac{1}{3^3}-\dfrac{1}{3^3}\right)+...+\left(\dfrac{1}{3^{99}}-\dfrac{1}{3^{99}}\right)+\left(\dfrac{1}{3}-\dfrac{1}{3^{100}}\right)=\dfrac{1}{3}-\dfrac{1}{3^{100}}\)
\(\Rightarrow2A=3\cdot\left(\dfrac{1}{3}-\dfrac{1}{3^{100}}\right)\)
\(\Rightarrow\text{A}=\dfrac{1-\dfrac{1}{3^{99}}}{2}\)
\(\Rightarrow A=\dfrac{1}{2}-\dfrac{1}{2.3^{99}}< \dfrac{1}{2}\)
\(A=\frac{14^{16}-21^{32}.35^{68}}{10^{16}.15^2.7^{96}}=\frac{2^{16}.7^{16}-3^{32}.7^{32}.7^{68}.5^{68}}{5^{16}.2^{16}.3^2.5^2.7^{96}}\)
\(A=\frac{2^{16}.7^{16}-3^{32}.7^{100}.5^{68}}{5^{18}.2^{16}.3^2.7^{96}}=\frac{7^{16}.\left(2^{16}-3^{32}.7^{84}.5^{68}\right)}{5^{18}.2^{16}.3^2.7^{96}}=\frac{2^{16}-3^{32}.7^{84}.5^{68}}{5^{18}.2^{16}.3^2.7^{88}}\)
\(B=\frac{4^{20}-2^{20}+6^{20}}{6^{20}-3^{20}+9^{20}}=\frac{2^{40}-2^{20}+2^{20}.3^{20}}{2^{20}.3^{20}-3^{20}+3^{40}}=\frac{2^{20}.\left(2^{20}-1+3^{20}\right)}{3^{20}.\left(2^{20}-1+3^{20}\right)}\)
\(B=\frac{2^{20}}{3^{20}}\)
a) \(3.5^2+15.2^2-26\div2\)
= 3.25 + 15.4 - 13
= 75 + 60 - 13
= 135 - 13
= 122
b) \(5^3.2-100\div4+2^3.5\)
= 125.2 - 25 + 8.5
= 250 - 25 + 40
= 225 + 40
= 265
c)\(6^2\div9+50.2-3^3.33\)
= 36 : 9 + 100 - 9.33
= 4 + 100 - 297
= 104 - 297
= -193
d)\(3^2.5+2^3.10-81\div3\)
= 9.5 + 8.10 - 27
= 45 + 80 - 27
= 125 - 27
= 98
e) \(5^{13}\div5^{10}-25.2^2\)
= 53 - 25.4
= 125 - 100
= 25
f) \(20\div2^2+5^9\div5^8\)
= 20 : 4 + 5
= 5 + 5
= 10
a) 23.25 + 75.23 - 1300
= 23.(25 + 75) - 1300
= 23.100 - 1300
= 2300 - 1300
= 1000
b) 36 : 3² - 5.2²
= 36 : 9 - 5.4
= 4 - 20
= -16
c) 183 + 80 : [20 - 4.(5² - 24)]
= 183 + 80 : [20 - 4.(25 - 24)]
= 183 + 80 : (20 - 4.1)
= 183 + 80 : 16
= 183 + 5
= 188
d) (-125) - [148 + 5.(-25)]
= -125 - (148 - 125)
= -125 - 148 + 125
= (-125 + 125) - 148
= 0 - 148
= -148
a) 23.25 + 75.23 - 1300
= 23. (25+75) - 1300
= 23.100 - 1300
= 2300 - 1300 = 1000
b) 36 : 32 - 5 . 22
= 36: 9 - 5.4
= 4 - 20 = -16
c) 183 + 80 : [ 20 - 4 ( 52 - 24 ) ]
= 183 + 80: [20 - 4.(25-24)]
= 183 + 80 : [20 - 4.1)]
= 183 + 80: [20 - 4]
= 183 + 80:16
= 183 + 5 = 188
d) (-125) - [148 + 5 . (-25) ]
= -125 - 148 + 125
= (125 - 125) - 148
= 0 - 148 = -148
nhóm cứ hai số liên tiếp lại vs nhâu sẽ đk quy luật tổng của toàn số -2
A=2-4+6-8+10-12+14-16+18-20+22-24+26-28+30-32
A= (-2)+(-2)+(-2)+(-2)+(-2)+(-2)+(-2)+(-2)
A= -16
a) x = 2.
b) x = 7.
c) x= 12.
d) x= 45.
e) x = 18.
f) x = 10.
a) \(x+5=20-\left(12-7\right)\)
\(\Rightarrow x+5=20-5\)
\(\Rightarrow x+5=15\)
\(\Rightarrow x=15-5\)
\(\Rightarrow x=10\)
b) \(15-\left(3+2x\right)=2^2\)
\(\Rightarrow3+2x=15-4\)
\(\Rightarrow3+2x=11\)
\(\Rightarrow2x=11-3\)
\(\Rightarrow2x=8\)
\(\Rightarrow x=\dfrac{8}{2}\)
\(\Rightarrow x=4\)
c) \(-11-\left(19-x\right)=50\)
\(\Rightarrow19-x=-11-50\)
\(\Rightarrow19-x=-61\)
\(\Rightarrow x=61+19\)
\(\Rightarrow x=80\)
d) \(159-\left(25-x\right)=43\)
\(\Rightarrow25-x=159-43\)
\(\Rightarrow25-x=116\)
\(\Rightarrow x=25-116\)
\(\Rightarrow x=-91\)
e) \(\left(79-x\right)-43=-\left(17-52\right)\)
\(\Rightarrow\left(79-x\right)-43=52-17\)
\(\Rightarrow79-x-43=35\)
\(\Rightarrow36-x=35\)
\(\Rightarrow x=1\)
f) \(\left(7+x\right)-\left(21-13\right)=32\)
\(\Rightarrow7+x-8=32\)
\(\Rightarrow x-1=32\)
\(\Rightarrow x=32+1\)
\(\Rightarrow x=33\)
g) \(-x+20=-15+8+13\)
\(\Rightarrow-x+20=6\)
\(\Rightarrow x=20-6\)
\(\Rightarrow x=14\)
h) \(-\left(-x+13-142\right)+18=55\)
\(\Rightarrow x-13+142+18=55\)
\(\Rightarrow x+147=55\)
\(\Rightarrow x=55-147\)
\(\Rightarrow x=-92\)
22 . ( x - 32 ) + 4 = 20
=> 4 . ( x + 9 ) = 16
=> x + 9 = 4
=> x = -5
\(2^2.\left(x-3^2\right)+4=20\)
\(4.\left(x-9\right)=20-4\)
\(4.\left(x-9\right)=16\)
\(\Rightarrow x-9=4\)
\(\Rightarrow x=13\)