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1. 11(x-9)=77
x-9=7
x=16
2. 4(x-3)=48
x-3=12
x=15
3.3(x-8)=81
(x-8)=27
x=35
Bài 1
S₂ = 21 + 23 + 25 + ... + 1001
Số số hạng của S₂:
(1001 - 21) : 2 + 1 = 491
⇒ S₂ = (1001 + 21) . 491 : 2 = 250901
--------
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) 7/38 x 9/11 +7/38 x 4/11 -7/38 x 2/11
=7/38.(9/11+4/11-2/11)
=7/38
B) 5/31 x 21/25 + 5/31 x -7/10 - 5/31 x 9/20
=5/31.(21/25-7/10-9/20)
=5/31.(-31/100)
=-1/20
1) x - 2 = -6
x = -6 + 2
x = -4
2) -5 . x - ( -3 ) =13
-5 . x = 13 + ( -3 )
-5 . x = 10
x = 10 : ( -5 )
x = -2
\(a.\dfrac{6}{5}=\dfrac{18}{x}\Rightarrow x=\dfrac{18\cdot5}{6}=15\\ \text{Vậy}\text{ }x=15.\)
\(b.\dfrac{3}{4}=\dfrac{-21}{x}\Rightarrow x=\dfrac{-21\cdot4}{3}=28\\ \text{ }\text{ }\text{ }\text{ }\text{Vậy }x=28.\)
\(c.\dfrac{x}{4}=\dfrac{21}{28}\Rightarrow x=\dfrac{21\cdot4}{28}=3\\ \text{Vậy }x=3.\)
\(d.\dfrac{-8}{2x}=\dfrac{3}{-9}\Rightarrow x=\dfrac{-8\cdot\left(-9\right)}{3}:2=12\\ \text{Vậy }x=12.\)
\(e.\dfrac{-4}{11}=\dfrac{x}{22}=\dfrac{40}{z}\\ \Rightarrow x=\dfrac{-4\cdot22}{11}=-8\\ \Rightarrow z=\dfrac{22\cdot40}{-8}=-110\\ \text{Vậy }x=-8;z=-110.\)
\(f.\dfrac{-3}{4}=\dfrac{x}{20}=\dfrac{21}{y}\\ \Rightarrow x=\dfrac{-3\cdot20}{4}=-15\\ \Rightarrow y=\dfrac{21\cdot20}{-15}=-28\\ \text{Vậy }x=-15;y=-28.\)
\(g.\dfrac{-4}{8}=\dfrac{x}{-10}=\dfrac{-7}{y}=\dfrac{z}{-24}\\ \Rightarrow x=\dfrac{-4\cdot\left(-10\right)}{8}=5\\ \Rightarrow y=\dfrac{-7\cdot\left(-10\right)}{5}=14\\ \Rightarrow z=\dfrac{-7\cdot\left(-24\right)}{14}=12\\ \text{Vậy }x=5;y=14;z=12.\)
\(h.\dfrac{x}{4}=\dfrac{9}{x}\\ \Rightarrow x\cdot x=9\cdot4\\ \Rightarrow x\cdot x=36\\ \Rightarrow x\cdot x=6\cdot6\\ \text{Vậy }\text{cả hai }x=6.\)
`#040911`
`a,`
`15 + 25 \div (2x - 1) = 20`
`\Rightarrow 25 \div (2x - 1) = 20 - 15`
`\Rightarrow 25 \div (2x - 1) = 5`
`\Rightarrow 2x - 1 = 25 \div 5`
`\Rightarrow 2x - 1 = 5`
`\Rightarrow 2x = 6`
`\Rightarrow x = 3`
Vây, `x = 3.`
`b,`
\(3^{x-1}+2\cdot3^x=21\)
`\Rightarrow 3^x \div 3 + 2. 3^x = 21`
`\Rightarrow 3^x . \frac{1}{3} + 2. 3^x = 21`
`\Rightarrow 3^x . (\frac{1}{3} + 2) = 21`
`\Rightarrow 3^x . \frac{7}{3} = 21`
`\Rightarrow 3^x = 21 \div \frac{7}{3}`
`\Rightarrow 3^x = 9`
`\Rightarrow 3^x = 3^2`
`\Rightarrow x = 2`
Vậy, `x = 2.`
`c,`
\(2^{x-3}+2^{x+1}=17\)
`\Rightarrow 2^x \div 2^3 + 2^x . 2 = 17`
`\Rightarrow 2^x . \frac{1}{8} + 2^x . 2 = 17`
`\Rightarrow 2^x . (\frac{1}{8} + 2) = 17`
`\Rightarrow 2^x . \frac{17}{8} = 17`
`\Rightarrow 2^x = 17 \div \frac{17}{8}`
`\Rightarrow 2^x = 8`
`\Rightarrow 2^x = 2^3`
`\Rightarrow x = 3`
Vậy, `x = 3`
`d,`
\(5^x-5^{x-1}=20\)
`\Rightarrow 5^x - 5^x \div 5 = 20`
`\Rightarrow 5^x - 5^x . \frac{1}{5} = 20`
`\Rightarrow 5^x . (1 - \frac{1}{5} = 20`
`\Rightarrow 5^x . \frac{4}{5} = 20`
`\Rightarrow 5^x = 20 \div \frac{4}{5}`
`\Rightarrow 5^x = 25`
`\Rightarrow 5^x = 5^2`
`\Rightarrow x = 2`
Vậy, `x = 2.`
\(a.25:\left(2x-1\right)=5\)
\(2x-1=5\Leftrightarrow2x=6\Leftrightarrow x=3\)
\(b.3^x:3+2.3^x=21\)\(\Leftrightarrow3^x.\dfrac{1}{3}+2.3^x=21\)
\(\Leftrightarrow3^x\left(\dfrac{1}{3}+2\right)=21\)
\(\Leftrightarrow3^x.\dfrac{7}{3}=21\)
\(\Leftrightarrow3^x=9\Leftrightarrow x=2\)
\(c.2^x:2^3+2^x.2=17\Leftrightarrow2^x.\dfrac{1}{8}+2^x.2=17\)
\(\Leftrightarrow2^x.\dfrac{17}{8}=17\Leftrightarrow2^x=8\Leftrightarrow x=3\)
\(d.5^x-5^x:5=20\Leftrightarrow5^x-5^x.\dfrac{1}{5}=20\)
\(\Leftrightarrow5^x\left(1-\dfrac{1}{5}\right)=20\Leftrightarrow5^x=20:\dfrac{4}{5}\Leftrightarrow5^x=25\Leftrightarrow x=2\)
\(T=1\cdot2\cdot3+2\cdot3\cdot4+...+20\cdot21\cdot22\)
\(4T=1\cdot2\cdot3\cdot4+2\cdot3\cdot4\cdot4+...+20\cdot21\cdot22\cdot4\)
\(4T=1\cdot2\cdot3\cdot\left(4-0\right)+2\cdot3\cdot4\cdot\left(5-1\right)+..+20\cdot21\cdot22\cdot\left(23-19\right)\)
\(4T=0\cdot1\cdot2\cdot3-1\cdot2\cdot3\cdot4+2\cdot3\cdot4\cdot5-1\cdot2\cdot3\cdot4+..+20\cdot21\cdot22\cdot23-19\cdot20\cdot21\cdot22\)
\(4T=21\cdot22\cdot23\cdot24\)
\(T=\frac{21\cdot22\cdot23\cdot24}{4}=21\cdot22\cdot23\cdot6=63756\\ k.cho.mk.nha\)
1.2.3+2.3.4+3.4.5+...+20.21.22
=1/4.(1.2.3.4+2.3.4.4+3.4.5.4+...+20.21.22.4)
=1/4.[1.2.3.(4-0)+2.3.4.(5-1)+3.4.5.(6-2)+...+20.21.22.(23-19)]
=1/4.(1.2.3.4+2.3.4.5-1.2.3.4+3.4.5.6-2.3.4.5+....-19.20.21.22+20.21.22.23)
=1/4.20.21.22.23
=53130