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a) \(\left(2x-1\right)^4=16\)
\(\)TH1: \(\left(2x-1\right)^4=2^4\)
\(=>2x-1=2\)
\(2x=2+1\)
\(2x=3\)
\(x=\dfrac{3}{2}\)
TH2: \(\left(2x-1\right)^4=\left(-2\right)^4\)
\(=>2x-1=-2\)
\(2x=-2+1\)
\(2x=-1\)
\(x=\dfrac{-1}{2}\)
Vậy x = \(\dfrac{3}{2}\) hoặc x = \(\dfrac{-1}{2}\)
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b) \(\left(2x+1\right)^3=125\) ( mình nghĩ đề bài đúng là vầy )
\(\left(2x+1\right)^3=5^3\)
\(=>2x+1=5\)
\(2x=5-1\)
\(2x=4\)
\(x=4:2\)
\(x=2\)
Vậy x = \(2\)
\(\left(2x-1\right)^4=16=\left(\pm2\right)^4\\ =>\left[{}\begin{matrix}2x-1=2\\2x-1=-2\end{matrix}\right.\\ =>\left[{}\begin{matrix}x=\dfrac{3}{2}\\x=-\dfrac{1}{2}\end{matrix}\right.\)
\(\left(2x+1\right)^3=125=5^3\\ =>2x+1=1\\ =>x=2\)
\(\dfrac{2x}{15}+\dfrac{2x}{35}+\dfrac{2x}{63}+...+\dfrac{2x}{195}=\dfrac{4}{5}\\ x\cdot\left(\dfrac{2}{15}+\dfrac{2}{35}+\dfrac{2}{63}+...+\dfrac{2}{195}\right)=\dfrac{4}{5}\\ x\cdot\left(\dfrac{2}{3\cdot5}+\dfrac{2}{5\cdot7}+\dfrac{2}{7\cdot9}+...+\dfrac{2}{13\cdot15}\right)=\dfrac{4}{5}\\ x\cdot\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+...+\dfrac{1}{13}-\dfrac{1}{15}\right)=\dfrac{4}{5}\\ x\cdot\left(\dfrac{1}{3}-\dfrac{1}{15}\right)=\dfrac{4}{5}\\ x\cdot\dfrac{4}{15}=\dfrac{4}{5}\\ x=\dfrac{4}{5}:\dfrac{4}{15}\\ x=3\)
Gọi \(D=\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{8}-\dfrac{1}{16}+\dfrac{1}{32}-\dfrac{1}{64}\)
\(2D=1-\dfrac{1}{2}+\dfrac{1}{4}-\dfrac{1}{8}+\dfrac{1}{16}-\dfrac{1}{32}\\ 2D+D=\left(1-\dfrac{1}{2}+\dfrac{1}{4}-\dfrac{1}{8}+\dfrac{1}{16}-\dfrac{1}{32}\right)+\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{8}-\dfrac{1}{16}+\dfrac{1}{32}-\dfrac{1}{64}\right)\\ 3D=1-\dfrac{1}{2}+\dfrac{1}{4}-\dfrac{1}{8}+\dfrac{1}{16}-\dfrac{1}{32}+\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{8}-\dfrac{1}{16}+\dfrac{1}{32}-\dfrac{1}{64}\\ 3D=1-\dfrac{1}{64}< 1\\ \Rightarrow D=\dfrac{1-\dfrac{1}{64}}{3}< \dfrac{1}{3}\)
Vậy \(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{8}-\dfrac{1}{16}+\dfrac{1}{32}-\dfrac{1}{64}< \dfrac{1}{3}\)
\(\left(2x-1\right)^4=16=2^4=\left(-2\right)^4\\ Vậy:2x-1=2.hoặc.2x-1=-2\\ Vậy:2x=2+1=3.hoặc.2x=-2+1=-1\\ Vậy:x=\dfrac{3}{2}hoặc.x=-\dfrac{1}{2}\)
\(\left(2x+1\right)^3=125\\ \Rightarrow\left(2x+1\right)^3=5^3\\ \Rightarrow2x+1=5\\ \Rightarrow2x=4\\ \Rightarrow x=2.\\ b,\left(2x-1\right)^4=16\\ \Rightarrow\left(2x-1\right)^4=2^4\\ \Rightarrow2x-1=2\\ \Rightarrow2x=3\\ \Rightarrow x=\dfrac{3}{2}.\\ c,6.3^x-2.3^x=36\\ \Rightarrow3^x.\left(6-2\right)=36\\ \Rightarrow3^x.4=36\\ \Rightarrow3^x=9\\ \Rightarrow3^x=3^2\\ \Rightarrow x=2.\\ d,2^{x+1}-2^x=32\\ \Rightarrow2^x.\left(2-1\right)=32\\ \Rightarrow2^x=2^5\\ \Rightarrow x=5.\)
Tìm số nguyên x, biết:
1) -16 + 23 + x = - 16
7+x=-16
x=-16-7
x=-23
2) 2x – 35 = 15
2x=15+35
2x=50
x=50:2
x=25
3) 3x + 17 = 12
3x=12-17
3x=-5
x=-5/3
4) (2x – 5) + 17 = 6
2x-5=6-17
2x-5=-11
2x=-11+5
2x=-6
x=-6:2
x=-3
5) 10 – 2(4 – 3x) = -4
2(4-3x)=10-(-4)
2(4-3x)=14
4-3x=14:2
4-3x=7
3x=4-7
3x=-3
x=-3:3
x=-1
6) - 12 + 3(-x + 7) = -18
3(-x+7)=-18-(-12)
3(x+7)=-6
x+7=-6:3
x+7=-2
x=-2-7
x=-9
\(4^5:4^x=16\)
\(4^5:4^x=4^2\)
\(4^x=4^5:4^2\)
\(4^x=4^3\)
\(x=3\)
\(\left(2x+1\right)^3=27\)
\(\left(2x+1\right)^3=3^3\)
\(2x+1=3\)
\(2x=3-1\)
\(2x=2\)
\(x=2:2\)
\(x=1\)
a) (x - 2)^2 = 16
(x - 2)^2 = 4^2 = (-4)^2
=> x - 2 = 4 hoặc x - 2 = -4
- Nếu x - 2 = 4
=> x = 4 + 2 = 6
- Nếu x - 2 = -4
=> x = (-4) + 2 = -2
Vậy x = 6 hoặc x = -2
b) (2x - 1)^3 = 8
(2x - 1)^3 = 2^3
=>2x - 1 = 2
2x = 2 + 1 = 3
\(x=\frac{3}{2}\)
c) (2x - 1)^4 = 81
(2x - 1)^4 = 3^4=(-3)^4
=> 2x - 1 = 3 hoặc 2x - 1 = -3
- Nếu 2x - 1 = 3
=>2x = 3 + 1 = 4
=>x = 4 : 2 = 2
- Nếu 2x - 1 = -3
2x = (-3) + 1 = -2
x = -1
Vậy x = 2 hoặc x = -1
a) (2x-1)4 = 16
=> (2x-1)4 = 24 hoặc (-2)4
=>[2x−1=22x−1=−2⇒[2x=2+12x=−2+1⇒⎡⎢ ⎢⎣x=32x=−12
(2x-1)^4=16
2x-1=2
2x=3
x=3/2