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\(3\left(a-2a\right)^2=27\Leftrightarrow3\left(-a\right)^2=27\Leftrightarrow\left(-a\right)^2=\dfrac{27}{3}=9\)
\(\Leftrightarrow\left\{{}\begin{matrix}-a=3\\-a=-3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}a=-3\\a=3\end{matrix}\right.\) vậy \(x=3;x=-3\)
\(A=3+3^2+3^3+...+3^{1010}\\ \Rightarrow3A=3^2+3^3+3^4+...+3^{1011}\\ \Rightarrow3A-A=3^{1011}-3\\ \Rightarrow2A+3=3^{1011}=27^{337}\left(đfcm\right)\)
Câu 1
a)(-9)+(-3) = -9 - 3 = -12
b)6.7.52+42.75 = 42. 25 + 42. 75 = 42(25 + 75) = 42. 100 = 4200
c)4529-(186+4529) = 4529 - 186 - 4529 = -186
Câu 2
a)x-7=15
<=> x = 15 + 7
<=> x = 22
b)9+4.(x-5)=17
<=> 9 + 4x - 20 = 17
<=> 4x = 28
<=> x = 7
c)(x-3)3=27
<=> (x - 3)3 = 33
=> x - 3 = 3
<=> x = 6
Câu 1:
a) Ta có: (-9)+(-3)
=-(9+3)
=-12
b) Ta có: \(6\cdot7\cdot5^2+42\cdot75\)
\(=6\cdot7\cdot5^2+6\cdot7\cdot5^2\cdot3\)
\(=6\cdot7\cdot5^2\cdot\left(1+3\right)\)
\(=6\cdot7\cdot25\cdot4\)
\(=42\cdot100=4200\)
c) Ta có: 4529-(186+4529)
=4529-186-4529
=-186
Câu 2:
a) Ta có: x-7=15
\(\Leftrightarrow x=15+7\)
hay x=22
Vậy: x=22
b) Ta có: \(9+4\left(x-5\right)=17\)
\(\Leftrightarrow9+4x-20=17\)
\(\Leftrightarrow4x-11=17\)
\(\Leftrightarrow4x=28\)
hay x=7
Vậy: x=7
c) Ta có: \(\left(x-3\right)^3=27\)
\(\Leftrightarrow\left(x-3\right)^3=3^3\)
\(\Leftrightarrow x-3=3\)
hay x=6
Vậy: x=6
e) \(3a+15⋮3a-1\)
=> \(3a-1+16⋮3a-1\)
Mà \(3a-1⋮3a-1\)
=> \(16⋮3a-1\)
.............
a) \(a+11⋮a+3\)
\(\Rightarrow\left(a+3\right)+8⋮a+3\)
Mà \(a+3⋮a+3\)
=> \(8⋮a+3\)
=> \(a+3\in\text{Ư}\left(8\right)=\left\{\text{ }\pm1;\pm2\pm4;\pm8\right\}\)
=> \(a\in\left\{-4;-2;-5;-1;-7;1;-11;5\right\}\)
c) {[(20 - 2.3).5] - 2.5} : 2 + (4.5)²
= {(20 - 6).5] - 10} : 2 + 20²
= (14.5 - 10) : 2 + 400
= (70 - 10) : 2 + 400
= 60 : 2 + 400
= 30 + 400
= 430
d) (1² + 2² + 3² + ... + 100²) . (2⁴ - 4²)
= (1² + 2² + 3² + ... + 100²) . (16 - 16)
= (1² + 2² + 3² + ... + 100²) . 0
= 0
Bài 2
a) -2x < 5
2x > 5
x > 5/2
b) [31 - (x + 5)].11 = 121
31 - (x + 5) = 121 : 11
31 - (x + 5) = 11
x + 5 = 31 - 11
x + 5 = 20
x = 20 - 5
x = 15
c) (x + 1)³ = 27
(x + 1)³ = 3³
x + 1 = 3
x = 3 - 1
x = 2