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Bài 2:
a, 7,2: 2,4.\(x\) = 45
3.\(x\) = 45
\(x\) = 45: 3
\(x\) = 15
b, 9,15.\(x\) + 2,85.\(x\) = 48
\(x\).( 9,15 + 2,85) = 48
12\(x\) = 48
\(x\) = 48: 12
\(x\) = 4
c) (x.3 + 4) : 5 = 8
x.3 + 4 = 8 x 5
x.3 + 4 = 40
x.3 = 40 - 4
x.3 = 36
x = 36 : 3
x = 12
A tính theo công thức tính tổng dãy số cách đều có khoảng cách là 3 (cấp số cộng có d=3)
\(3C=2x3x3+3x4x3+4x5x3+5x6x3+...x199x200x3+200x201x3\)
\(3C=2x3x\left(4-1\right)+3x4x\left(5-2\right)+4x5x\left(6-3\right)+...+200x201\left(202-199\right)\)
3C=--1x2x3+2x3x4-2x3x4+3x4x5-3x4x5+4x5x6-...-199x200x201+200x201x202
3C=200x201x202-1x2x3=> C=(200x201x202-1x2x3):3=200x67x202-2
a) \(2^x.4=128\Rightarrow2^x=32=2^5\Rightarrow x=5\)
b) \(x^{17}=x\Rightarrow x^{17}-x=0\Rightarrow x\left(x^{16}-1\right)=0\Rightarrow x=0\) hay \(x=1\)
c) \(\left(2x-2\right)^3=8\Rightarrow\left(2x-2\right)^3=2^3\Rightarrow2x-2=2\Rightarrow2x=4\Rightarrow x=2\)
d) \(\left(x-6\right)^3=\left(x-6\right)^2\Rightarrow\left(x-6\right)^3-\left(x-6\right)^2=0\)
\(\Rightarrow\left(x-6\right)^2\left(x-6-1\right)=0\Rightarrow\Rightarrow\left(x-6\right)^2\left(x-7\right)=0\)
\(\Rightarrow x-6=0\) hay \(x-7=0\Rightarrow x=6\) hay \(x=7\)
e) \(\left(7x-11\right)^3=2^5.5^2+200\Rightarrow\left(7x-11\right)^3=32.25+200\)
\(\Rightarrow\left(7x-11\right)^3=1000=10^3\Rightarrow7x-11=10\Rightarrow7x=21\Rightarrow x=3\)
f) \(3+2^{x-1}=24-\left[4^2-\left(2^2-1\right)\right]\Rightarrow2^{x-1}=24-\left[16-3\right]-3\)
\(\Rightarrow2^{x-1}=24-13-3\Rightarrow2^{x-1}=8=2^3\Rightarrow2x-1=3\Rightarrow2x=4\Rightarrow x=2\)
\(\left(7x-11\right)^3=2^5.5^2+200\)
\(\left(7x-11\right)^3=1000=10^3\)
=> 7x-11=10
=> 7x=10+11
=> 7x=21
=> x=21:7
=> x= 3
\(x^{20}=1^x \Rightarrow x=1\)
\(x^{10}=x \Rightarrow x=0;1\)
a: =>3x-15-2x+6=51
=>x-9=51
=>x=60
b: =>432-2x+22+3x-15=200
=>x+439=200
=>x=-239
c: =>3x+17-4x+13=0
=>30-x=0
=>x=30
d: =>x-3-3x+6=-11-21=-32
=>-2x+3=-32
=>-2x=-35
=>x=35/2
\(3\cdot\left(x-5\right)-2\cdot\left(x-3\right)=51\)
\(\Rightarrow3x-15-2x+6=51\)
\(\Rightarrow x-9=51\)
\(\Rightarrow x=51+9\)
\(\Rightarrow x=60\)
b) \(432-2\cdot\left(x-11\right)+3\cdot\left(x-5\right)=200\)
\(\Rightarrow432-2x+22+3x-15=200\)
\(\Rightarrow x+439=200\)
\(\Rightarrow x=200-439\)
\(\Rightarrow x=-239\)
c) \(3x+17=4x-13\)
\(\Rightarrow4x-3x=17+13\)
\(\Rightarrow x=30\)
d) \(\left(x-3\right)+21=3\cdot\left(x-2\right)-11\)
\(\Rightarrow x-3+21=3x-6-11\)
\(\Rightarrow x+18=3x-17\)
\(\Rightarrow3x-x=18+17\)
\(\Rightarrow2x=35\)
\(\Rightarrow x=\dfrac{35}{2}\)