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b) 3x - 6 - (8x + 4) - (10x + 15) = 50
=> 3x - 6 - 8x - 4 - 10x - 15 = 50
=> (3x - 8x - 10x) = 6+ 4 + 15 + 50
=> -15x = 75 => x = 75 : (-15) = -5
c) => 2x - 3 = 2 - x hoặc 2x - 3 = - (2 - x) (Vì 2 số có giá trị tuyệt đối bằng nhau thì chings bằng nhau hoặc đối nhau)
+) nếu 2x - 3 = 2 - x => 2x+ x = 2 + 3 => 3x = 5 => x = 5/3
+) nếu 2x - 3 = -(2 - x) => 2x - 3 = -2 + x => 2x - x = -2 + 3 => x = 1
Vậy x = 5/3 hoặc x = 1
a) (n-1)n+11-(n-1)n=0
(n-1)n(n-1)11-(n-1)n=0
(n-1)n[(n-1)11-1]=0
(n-1)n=0 hoặc (n-1)11-1=0
n-1=0 hoặc (n-1)11 =1
n=1 hoặc n-1 =1
n=1 hoặc n =2
\(\left(x+2\right)^{n+1}=\left(x+2\right)^{n+11}\)
\(\Leftrightarrow\orbr{\begin{cases}x+2=1\\x+2=0\end{cases}\Rightarrow\orbr{\begin{cases}x=-1\\x=-2\end{cases}}}\)
\(\left(x+2\right)^{n+1}-\left(x+2\right)^{x+11}=0\\ \Leftrightarrow\left(x+2\right)^{n+1}\left(1-\left(x+2\right)^{10}\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}\left(x+2\right)^{n+1}=0\\1-\left(x+2\right)^{10}=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=-2\\\left(x+2\right)^{10}=1\Rightarrow x+2=-1\Rightarrow x=-3\end{cases}}}\)
\(\left(x+2\right)^{n+1}=\left(x+2\right)^{n+11}\)
\(\Leftrightarrow\left(x+2\right)^{n+1}-\left(x+2\right)^{n+11}=0\)
\(\Leftrightarrow\left(x+2\right)^{n+1}-\left(x+2\right)^{n+1}\cdot\left(x+2\right)^{10}=0\)
\(\Leftrightarrow\left(x+2\right)^{n+1}\left[1-\left(x+2\right)^{10}\right]=0\)
\(\Leftrightarrow\orbr{\begin{cases}\left(x+2\right)^{n+1}=0\\1-\left(x+2\right)^{10}=0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x+2=0\\x+2\in\left\{\pm1\right\}\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=-2\\x\in\left\{-1;-3\right\}\end{cases}}\)
Vậy....
=> (x+2)n+11:(x+2)n+1=1
<=> (x+2)10=1
th1:x+2=1
<=>x=-1
th2:x+2=-1
<=>x=-3
vậy x=-1 hoặc x=-3
\(M\left(x\right)+N\left(x\right)\)
\(=5x^3-x^2-4+2x^4-2x^2+2x+1\)
\(=2x^4+5x^3-3x^2+2x-3\)
\(M\left(x\right)-N\left(x\right)\)
\(=5x^3-x^2-4-\left(2x^4-2x^2+2x+1\right)\)
\(=5x^3-x^2-4-2x^4+2x^2-2x-1\)
\(=-2x^4+5x^3+x^2-2x-5\)
\(M\left(x\right)+P\left(x\right)=N\left(x\right)\)
\(\Rightarrow P\left(x\right)=N\left(x\right)-M\left(x\right)\)
\(\Rightarrow P\left(x\right)=2x^4-2x^2+2x+1-\left(5x^3-x^2-4\right)\)
\(\Rightarrow P\left(x\right)=2x^4-2x^2+2x+1-5x^3+x^2+4\)
\(\Rightarrow P\left(x\right)=2x^4-5x^3-x^2+2x+5\)
\(\left(x+2\right)^{n+1}=\left(x+2\right)^{n+11}\)
\(\Rightarrow\left(x+2\right)^{n+11}-\left(x+2\right)^{n+1}=0\)
\(\Rightarrow\left(x+2\right)^{n+1}\left[\left(x+2\right)^{10}-1\right]=0\)
\(\Rightarrow\left[{}\begin{matrix}\left(x+2\right)^{n+1}=0\\\left(x+2\right)^{10}-1=0\end{matrix}\right.\)
+) \(\left(x+2\right)^{n+1}=0\Rightarrow x+2=0\Rightarrow x=-2\)
+) \(\left(x+2\right)^{10}-1=0\Rightarrow\left(x+2\right)^{10}=1\)
\(\Rightarrow\left[{}\begin{matrix}x+2=1\\x+2=-1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-1\\x=-3\end{matrix}\right.\)
Vậy \(x\in\left\{-2;-1;-3\right\}\)
a,
- Theo đề bài ta có:
(8x-1)2n-1 = 52n-1
=> 8x-1 = 5
8x = 6
x = \(\dfrac{6}{8}\)= \(\dfrac{3}{4}\)
- Vậy x = \(\dfrac{3}{4}\)
b,
- Ta có:
(x - 7)x+1 - (x - 7)x+11 = 0
(x - 7)x . (x - 7) - (x - 7)x . (x - 7)11 = 0
(x - 7)x . [(x - 7) - (x - 7)11] = 0
=> (x - 7)x = 0 hoặc [(x - 7) - (x - 7)11] = 0
- TH1: (x - 7)x = 0
=> x - 7 = 0
=> x = 7
- TH2:
[(x - 7) - (x - 7)11] = 0
=> x - 7 = (x -7)11
=> x - 7 = 1 hoặc x - 7 = 0
+ Nếu x - 7 = 1
x = 8
+ Nếu x - 7 = 0 (TH1)
- Vậy x = 7 hoặc x = 8
c, - Theo đề bài ta có:
\(\left(x-\dfrac{2}{9}\right)^3=\left(\dfrac{2}{3}\right)^6\)
- Thấy \(\left(\dfrac{2}{3}\right)^6=\left(\dfrac{2}{3}\right)^{2\cdot3}\)= \(\left(\dfrac{4}{9}\right)^3\)
=> \(\left(x-\dfrac{2}{9}\right)^3=\left(\dfrac{4}{9}\right)^3\)
=> \(x-\dfrac{2}{9}=\dfrac{4}{9}\)
=> \(x=\dfrac{4}{9}-\dfrac{2}{9}\)
\(x=\dfrac{2}{9}\)
- Vậy \(x=\dfrac{2}{9}\)
1.
a) \(x\in\left\{4;5;6;7;8;9;10;11;12;13\right\}\)
b) x=0
d) \(x=\frac{-1}{35}\) hoặc \(x=\frac{-13}{35}\)
e) \(x=\frac{2}{3}\)