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22 tháng 10 2019
1. \(6x^3-8=40\\ 6x^3=48\\ x^3=8\\ \Rightarrow x=2\)Vậy x = 2
2. \(4x^5+15=47\\ 4x^5=32\\ x^5=8\\ \Rightarrow x\in\varnothing\left(\text{vì }x\in N\right)\)Vậy x ∈ ∅
3. \(2x^3-4=12\\ 2x^3=16\\ x^3=8\\ \Rightarrow x=2\)Vậy x = 2
4. \(5x^3-5=0\\ 5x^3=5\\ x^3=1\\ \Rightarrow x=1\)Vậy x = 1
5. \(\left(x-5\right)^{2016}=\left(x-5\right)^{2018}\\ \Rightarrow\left[{}\begin{matrix}x-5=0\\x-5=1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=5\\x=6\end{matrix}\right.\)Vậy \(x\in\left\{5;6\right\}\)
6. \(\left(3x-2\right)^{20}=\left(3x-1\right)^{20}\\ \Rightarrow3x-2=3x-1\\ 3x-3x=2-1\\ 0=1\left(\text{vô lí}\right)\)Vậy x ∈ ∅
7. \(\left(3x-1\right)^{10}=\left(3x-1\right)^{20}\\ \left(3x-1\right)^{10}=\left[\left(3x-1\right)^2\right]^{10}\\ \Rightarrow\left(3x-1\right)^2=3x-1\\ \left(3x-1\right)^2-\left(3x-1\right)=0\\ \left(3x-1\right)\left[\left(3x-1\right)-1\right]=0\\ \left(3x-1\right)\left(3x-2\right)=0\\ \Rightarrow\left[{}\begin{matrix}3x-1=0\\3x-2=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}3x=1\\3x=2\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\frac{1}{3}\left(\text{loại vì }x\in N\right)\\x=\frac{2}{3}\left(\text{loại vì }x\in N\right)\end{matrix}\right.\)Vậy x ∈ ∅
8. \(\left(2x-1\right)^{50}=2x-1\\ \left(2x-1\right)^{50}-\left(2x-1\right)=0\\ \left(2x-1\right)\left[\left(2x-1\right)^{49}-1\right]=0\\ \Rightarrow\left[{}\begin{matrix}2x-1=0\\\left(2x-1\right)^{49}=1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}2x=1\\2x-1=1\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=\frac{1}{2}\left(\text{loại vì }x\in N\right)\\x=1\left(t/m\right)\end{matrix}\right.\)Vậy x = 1
9. \(\left(\frac{x}{3}-5\right)^{2000}=\left(\frac{x}{3}-5\right)^{2008}\\ \left(\frac{x}{3}-5\right)^{2008}-\left(\frac{x}{3}-5\right)^{2000}=0\\ \left(\frac{x}{3}-5\right)^{2000}\left[\left(\frac{x}{3}-5\right)^8-1\right]=0\\ \Rightarrow\left[{}\begin{matrix}\left(\frac{x}{3}-5\right)^{2000}=0\\\left(\frac{x}{3}-5\right)^8=1\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}\frac{x}{3}-5=0\\\frac{x}{3}-5=1\\\frac{x}{3}-5=-1\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}\frac{x}{3}=5\\\frac{x}{3}=6\\\frac{x}{3}=4\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=5\cdot3=15\\x=6\cdot3=18\\x=4\cdot3=12\end{matrix}\right.\)Vậy \(x\in\left\{15;18;12\right\}\)
22 tháng 10 2019
\(1.6x^3-8=40\\ \Leftrightarrow6x^3=48\\ \Leftrightarrow x^3=8\Leftrightarrow x^3=2^3=\left(-2\right)^3\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-2\end{matrix}\right.\)
Vậy \(x\in\left\{2;-2\right\}\)
\(2.4x^3+15=47\) (T nghĩ đề là mũ 3)
\(\Leftrightarrow4x^3=32\Leftrightarrow x^3=8=2^3=\left(-2\right)^3\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-2\end{matrix}\right.\)
Vậy \(x\in\left\{2;-2\right\}\)
Câu 3, 4 tương tự nhé.
14 tháng 10 2018
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2 tháng 8 2021
Bài 1:
a) Ta có: \(\left(2x-1\right)^{20}=\left(2x-1\right)^{18}\)
\(\Leftrightarrow\left(2x-1\right)^{20}-\left(2x-1\right)^{18}=0\)
\(\Leftrightarrow\left(2x-1\right)^{18}\left[\left(2x-1\right)^2-1\right]=0\)
\(\Leftrightarrow\left(2x-1\right)^{18}\cdot\left(2x-2\right)\cdot2x=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{1}{2}\\x=1\end{matrix}\right.\)
b) Ta có: \(\left(2x-3\right)^2=9\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-3=3\\2x-3=-3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=6\\2x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=0\end{matrix}\right.\)
c) Ta có: \(\left(x-5\right)^2=\left(1-3x\right)^2\)
\(\Leftrightarrow\left(x-5\right)^2-\left(3x-1\right)^2=0\)
\(\Leftrightarrow\left(x-5-3x+1\right)\left(x-5+3x-1\right)=0\)
\(\Leftrightarrow\left(-2x-4\right)\left(4x-6\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-2\\x=\dfrac{3}{2}\end{matrix}\right.\)
2 tháng 8 2021
Bài 2:
a) \(15^{20}-15^{19}=15^{19}\left(15-1\right)=15^{19}\cdot14⋮14\)
b) \(3^{20}+3^{21}+3^{22}=3^{20}\left(1+3+3^2\right)=3^{20}\cdot13⋮13\)
c) \(3+3^2+3^3+...+3^{2007}\)
\(=3\left(1+3+3^2\right)+...+3^{2005}\left(1+3+3^2\right)\)
\(=13\left(3+...+3^{2005}\right)⋮13\)
16 tháng 10 2021
A) \(X+15=4^2\)
=> \(X=16-15\)
=> \(X=1\)
b) 100 : ( 35 - X ) = 5
=> 35 - X = 100 : 5
=> 35 - X = 20
=> X = 35 - 20
=> X = 15
C) \(3X-17=2^2\cdot2^4\)
=> \(3X-17=2^6=64\)
=> \(3X=64+17\)
=> \(3X=81\)
=> \(X=27\)
d) 120 - 20 ( 50 - 4X ) = 0
=> 20 ( 50 - 4X ) = 120
=> 50 - 4X = 120 : 20
=> 50 - 4X = 6
=> 4X = 50 - 6
=> 4X = 44
=> X = 11
26 tháng 2 2021
a) \(-28-7|-3x+15|=-70\)
\(\Rightarrow7|-3x+15|=42\)
\(\Rightarrow|-3x+15|=6\)
\(\Rightarrow|3\left(5-x\right)|=6\)
\(\Rightarrow|3|.|5-x|=6\)
\(\Rightarrow3|5-x|=6\)
\(\Rightarrow|5-x|=2\)
\(\Rightarrow\orbr{\begin{cases}5-x=2\\5-x=-2\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=3\\x=7\end{cases}}\)
Vậy \(x\in\left\{3;7\right\}\)
b) \(|18-2|-x+5||=12\)
\(\Rightarrow\orbr{\begin{cases}18-2|-x+5|=12\\18-2|-x+5|=-12\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}2|5-x|=6\\2|5-x|=30\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}|5-x|=3\left(1\right)\\|5-x|=15\left(2\right)\end{cases}}\)
Từ \(\left(1\right):\Rightarrow\orbr{\begin{cases}5-x=3\\5-x=-3\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=2\\x=8\end{cases}}\)
Từ \(\left(2\right):\Rightarrow\orbr{\begin{cases}5-x=15\\5-x=-15\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=-10\\x=20\end{cases}}\)
Vậy \(x\in\left\{2;8;-10;20\right\}\)
c) \(12-2\left(-x+3\right)^2=-38\)
\(\Rightarrow2\left(3-x\right)^2=50\)
\(\Rightarrow\left(3-x\right)^2=100\)
\(\Rightarrow\orbr{\begin{cases}3-x=10\\3-x=-10\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=-7\\x=13\end{cases}}\)
Vậy \(x\in\left\{-7;13\right\}\)
d) \(-20+3\left(2x+1\right)^3=-101\)
\(\Rightarrow3\left(2x+1\right)^3=-81\)
\(\Rightarrow\left(2x+1\right)^3=-27\)
\(\Rightarrow2x+1=-3\)
\(\Rightarrow2x=-4\)
\(\Rightarrow x=-2\)
Vậy \(x=-2\)
QA
27 tháng 2 2021
Trả lời:
a, -28 - 7| -3x + 15 | = -70
=> 7| -3x + 15 | = 42
=> | -3x + 15 | = 6
=> -3x + 15 = 6 hoặc -3x + 15 = -6
=> -3x = -9 -3x = -21
=> x = 3 x = 7
Vậy x = 3; x = 7
b, | 18 - 2 | -x + 5 || = 12
=> 18 - 2| -x + 5 | = 12 hoặc 18 - 2| -x + 5 | = -12
=> 2 | -x + 5 | = 6 hoặc 2 | -x + 5 | = 30
=> | -x + 5 | = 3 hoặc | -x + 5 | = 15
=> -x + 5 = 3 hoặc -x + 5 = -3 hoặc -x + 5 = 15 hoặc -x + 5 = -15
=> x = 2 x = 8 x = -10 x = 20
Vậy x \(\in\){ 2; 8; -10; 20 }
c, 12 - 2.( -x + 3 )2 = -38
=> 2.( -x + 3 )2 = 50
=> ( -x + 3 )2 = 25
=> -x + 3 = 5 hoặc -x + 3 = -5
=> x = -2 x = 8
Vậy x = -2; x = 8
d, -20 + 3.( 2x + 1 )3 = -101
=> 3.( 2x + 1)3 = -81
=> ( 2x + 1 )3 = -27
=> 2x + 1 = -3
=> 2x = -4
=> x = -2
Vậy x = -2
=> x = 1
VN
Võ Ngọc Phương
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2 tháng 1
a) \(\left(5x+3^4\right).6^8=6^9.3^4\)
\(=>6x+3^4=3^4.6^9:6^8\)
\(=>6x+3^4=3^4.6\)
\(=>6x=6.3^4-3^4\)
\(=>6x=0\)
\(=>x=0:6\)
\(=>x=0\)
2 tháng 1
a/(5x + 34).68=69.34
(5x + 34) = 69:68.34
5x + 81 = 6.81
5x = 6.81 - 81
5x = 486 - 81
5x = 425
x = 425:5
x = 85
b/92 - 2x = 2.42- 3.4 + 120:15
92 - 2x = 2.16 - 12 + 8
92 - 2x = 32 - 12 + 8
92 - 2x = 28
2x = 92 - 28
2x = 64
x = 64:2
x = 32
c/53.(3x + 2) : 13 = 103: (135:134)
125.(3x + 2) : 13 = 1000:13
125.(3x+2) = 1000:13.13
125.(3x+2) = 1000
3x + 2 = 1000:125
3x + 2 = 8
3x = 8 - 2
3x = 6
x = 6:3
x = 2
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17 tháng 12 2018
a)2(x - 2) + 7.(3 - x) = -2.(3x - 18)
=> 2x - 4 + 21 - 7x = -6x - 36
=> 2x - 7x + 6x = 36 - 21 + 4
=> x = 19