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20 . 2^x + 1 = 10.4^2 + 1
20 . 2^x + 1 = 10 . 16 + 1
20 . 2^x + 1 = 161
20 . 2^x = 161 - 1
20 . 2^x = 160
2^x = 8
2^x = 2^3
=> x = 3
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a) \(x+5.\left(-2\right)=3+\left(-5\right)\Leftrightarrow x-10=3-5\Leftrightarrow x=3-5+10=8\)
vậy \(x=8\)
b) \(2.x-4=5.\left(-4\right)\Leftrightarrow2x-4=-20\Leftrightarrow2x=-20+4=-16\Leftrightarrow x=\dfrac{-16}{2}=-8\)
vậy \(x=-8\)
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-(x - 5) + 2 = 4 - x
- x + 5 + 2 = 4 - x
- x + x = 4 - 5 - 2
0x = - 3
\(x\in\phi\)
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b) (x+2)5=210 c) 5x : 52 = 125 d) (3x-24) . 73= 2x74 ( câu a khá dài nên mình để sau nhé )
(x+2)5=45 5x : 52 = 53 (3x-24) . 73= 2x74 : 73
x+2=4 5x = 53 . 52 3x-24 = 2x7
x=4-2 5x = 55 3x -16 =14
x=2 x = 5 3x=14+16
3x=30
x=30:3
x=10
a) (x-5)4 = (x-5)6
(x-5)4 - (x-5)6 =0
(x-5)4 - (x-5)4 . (x-5)2 =0
(x-5)4 - [ 1- (x-5 )2 ] =0
TH1: ( x-5 )4 =0 TH2: 1-( x-5)2 = 0
x-5=0 (x-5)2 = 1-0
x=0+5 (x-5)2 =1
x=5 x-5 = +-1
* x-5=1
x=6
* x-5=-1
x=4
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a, \(\left|2x+1\right|=5\Rightarrow2x+1\in\left\{5;-5\right\}\)
+) Nếu :\(2x+1=5\Rightarrow2x=4\Rightarrow x=4\div2=2\)
+) Nếu : \(2x+1=-5\Rightarrow2x=-6\Rightarrow x=-6\div2=-3\)
Vậy \(x\in\left\{2;-3\right\}\)
b, \(\left|x-4\right|=\left|2-x\right|\)
\(\Rightarrow\left[\begin{matrix}x-4=2-x\\x-4=-\left(2-x\right)\end{matrix}\right.\)
+) Nếu : x - 4 = 2 - x
\(\Rightarrow x+x=2+4\Rightarrow2x=6\Rightarrow x=3\)
+) Nếu : x - 4 = - ( 2 - x )
\(\Rightarrow x-4=-2+x\Rightarrow x-x=-2+4\Rightarrow0=2\) ( loại )
Vậy x = 3 thỏa mãn đề bài
c, \(\left|x-5\right|=2-x\Rightarrow\left|x-5\right|+x=2\)
+) Nếu : \(x< 5\Rightarrow x-5< 5-5\Rightarrow x-5< 0\Rightarrow\left|x-5\right|=-x+5\)
Thay vào đề , ta có :
\(-x+5+x=2\Rightarrow-x+x+5=2\Rightarrow5=2\) ( loại )
+) Nếu : \(x\ge5\Rightarrow x-5\ge5-5\Rightarrow x-5\ge0\Rightarrow\left|x-5\right|=x-5\)
Thay vào đề , ta có :
\(\left(x-5\right)-x=2\Rightarrow x-5-x=2\)
\(\Rightarrow x-x-5=2\Rightarrow-5=2\) ( loại )
Vậy \(x\in\varnothing\)
\(\frac{3}{x-5}=-\frac{4}{x-2}\)
=> 3(x - 2) = -4(x - 5)
=> 3x - 6 = -4x + 20
=> 3x + 4x = 20 + 6
=> 7x = 26
=> x = 26/7
\(\frac{3}{x-5}=\frac{-4}{x-2}\)
=> 3(x-2) = -4 ( x - 5 )
=> 3x - 6 = -4x + 20
=> 7x = 26
=> x = \(\frac{26}{7}\)
Vậy ...