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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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mình làm cách cấp 1 nhé
(x+1)+(x+2)+(x+3)+........+(x+100)=5750
=> (x+x+...+x)+(1+2+3+...+100)=5750
=> (x.100)+(1+100).100:2=5750
=> (x.100)+5050=5750
=>x.100=5750-5050
=>x.100=700
=>x =700:100
x = 7
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\(\left(x+\frac{1}{2}\right).\left(x-\frac{3}{4}\right)=0\)
TH1:
\(x+\frac{1}{2}=0\)
=> x = \(\frac{-1}{2}\)
TH2:
\(x-\frac{3}{4}=0\)
=> x = \(\frac{3}{4}\)
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\(\frac{-2}{3}\left(x-\frac{1}{4}\right)=\frac{1}{3}\left(2x-1\right)\)\(\Leftrightarrow-2\left(x-\frac{1}{4}\right)=2x-1\)\(\Leftrightarrow-2x+\frac{1}{2}-2x+1=0\Leftrightarrow x=\frac{3}{8}\)
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nhận xét 3 >0
=> /3x+1/= 3x+1
/4-x/= 4-x
ta có 3x+1 + 4 -x = 3
=> 2x + 5 = 3
=> 2x = -2
=> x= -1
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\(\left(x-1\right)^4:3^2=3^6\)
\(\left(x-1\right)^4=3^6.3^2\)
\(\left(x-1\right)^4=3^8\)
\(\left(x-1\right)^4=3^{2.4}=\left(3^2\right)^4=9^4\)
\(\Rightarrow\orbr{\begin{cases}x-1=9\\x-1=-9\end{cases}\Rightarrow\orbr{\begin{cases}x=9+1=10\\x=-9+1=-8\end{cases}}}\)
Vậy: \(\orbr{\begin{cases}x=10\\x=-8\end{cases}}\)
( x - 1 )4 : 32 = 36
( x - 1 )4 = 36 . 32
( x - 1 )4 = 38
( x - 1 )4 = 6561
( x - 1 )4 = 94
x - 1 = 9
x = 10
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x - 0,5 = 1/3+1/4
=> x - 1/2 =1/3 +1/4
=>x - 6/12= 7/12
=>x = 13/12
|x - 1| + |x + 3| = 4
Nếu x >/ = 1
x - 1 + x + 3 = 4
2x + 2 = 4
x = 1
Nếu x < 1
-(x - 1) - (x+ 3) = 4
-x + 1 - x - 3 = 4
-2x - 2 = 4
-2x = 6
x = -3
Vậy x thuộc {-3 ; 1}
TH1: Cả 2 thừa số lớn hơn 1:
x - 1 + x + 3 = 4
=> ( x + x ) - ( 1 - 3 ) = 4
=> 2x + 2 = 4
=> 2x = 2
=> x = 1
TH2: x - 1 < 0 ; x + 3 > 0
-( x - 1 ) + x + 3 = 4
=> -x + 1 + x + 3 = 4
=> ( -x + x ) + ( 1 + 3 ) = 4
=> 0x + 4 = 4
=> 0x = 0
=> x = 0
TH3: x - 1 > 0 ; x + 3 < 0
=> x - 1 + -( x + 3 ) = 4
=> x - 1 - x - 3 = 4
=> ( x - x ) - ( 1 - 3 ) = 4
=> 0x + 2 = 4
=> 0x = 2 ( vô nghiệm )
TH4: Cả 2 thừa số bé hơn 0:
-( x - 1 ) + -( x + 3 ) = 4
=> -x + 1 - x - 3 = 4
=> ( -x - x ) + ( 1 - 3 ) = 4
=> -2x - 2 = 4
=> -2x = 6
=> x = -3
Vậy tập hợp nghiệm S = { 1 ; 0 ; -3 }