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a) 3x.3x+2 =81
3x.3x.32 =81
3x.3x.9 =81
3x.3x =81/9
3x.3x =9
31.31 =9
x =1
b)2(x+15)+3(x+25)=2050
2(x+15)+3(x+15+10)=2050
2(x+15)+3(x+15)+3.10=2050
(x+15)(2+5)+30=2050
(x+15)5=2050-30
(x+15)5=2020
x+15=2020/5
x+15=404
x =404-15
x =389
c)2x+2x+1+2x+2+2x+3=960
2x+2x.2+2x.22+2x.23=960
2x(1+2+22+23)=960
2x(1+2+4+8)=960
2x.15=960
2x =960/15
2x =64
26 =64
x =6
bài d làm tương tự c,e làm tương tự a
f)3x.32x+3=729
33x.33=729
33x.27 =729
33x =729/27
33x =27
33.1 =27
x =1
\(2^x+2^{x+1}+2^{x+2}=960-2^{x+3}\)
\(2^x+2^{x+1}+2^{x+2}+2^{x+3}=960\)
\(2^x.\left(1+2+2^2+2^3\right)=960\)
\(2^x.15=960\)
\(2^x=64\)
\(2^x=2^6\)
Vậy x=6
3 . ( 5x -1 ) - 2 = 70
3 . ( 5x -1 ) = 70 + 2
3 . ( 5x -1 ) = 72
5x -1 = 72 : 3
5x -1 = 24
5x = 24 + 1
5x = 25
5x = 52
=> x = 2
a, \(x+\left(x+1\right)+\left(x+2\right)+...+\left(x+90\right)=5450\)
\(\left(x+x+x+...+x\right)+\left(1+2+3+...+90\right)=5450\)
\(91x+4095=5450\)
\(91x=1355\)
\(x=\frac{1355}{91}\)
b, \(2^x+2^{x+1}+2^{x+2}=960-2^{x+3}\)
\(2^x+2^x.2+2^x.2^2+2^x.2^3=960\)
\(2^x\left(1+2+2^2+2^3\right)=960\)
\(2^x.15=960\)
\(2^x=64=2^6\)
\(\Rightarrow x=6\)
Bài làm
2x + 2x + 1 + 2x + 2 = 960 - 2x + 3
2x . 1 + 2x . 2 + 2x . 22 + 2x + 23 = 960
2x ( 1 + 2 + 22 + 23 ) = 960
2x ( 1 + 2 + 3 + 8 ) = 960
2x . 15 = 960
2x = 64
Mà 64 = 26
=> 2x = 26
Vậy x = 6
# Học tốt #
`Answer:`
a. \(\left(x-3\right)+\left(x-2\right)+\left(x-1\right)+...+9+10+11=11\)
\(\Leftrightarrow x-3+x-2+x-1+...+9+10+11=11\)
\(\Leftrightarrow3x+\left(-3-2-1+0+...+11\right)=11\)
\(\Leftrightarrow3x+60=11\)
\(\Leftrightarrow3x=-49\)
\(\Leftrightarrow x=-\frac{49}{3}\)
b. \(\left(x+1\right)+\left(x+2\right)+\left(x+3\right)+...+\left(x+100\right)=5750\)
\(\Leftrightarrow\left(x+x+x+...+x\right)+\left(1+2+3+...+100\right)=5750\)
\(\Leftrightarrow100x+[\left(100+1\right).100:2]=5750\)
\(\Leftrightarrow100x+5050=5750\)
\(\Leftrightarrow100x=700\)
\(\Leftrightarrow x=7\)
c. \(2^x+2^{x+1}+2^{x+2}=960-2^{x+3}\)
\(\Leftrightarrow2^x+2^x.2+2^x.2^2+2^x.2^3=960\)
\(\Leftrightarrow2^x+2.2^x+4.2^x+8.2^x=960\)
\(\Leftrightarrow2^x.\left(1+2+4+8\right)=960\)
\(\Leftrightarrow2^x.15=960\)
\(\Leftrightarrow2^x=64\)
\(\Leftrightarrow x=6\)
2x + 2x + 1 + 2x + 2 = 960 - 2x + 3
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MN giup mk vs
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Nhiều câu quá >.<
a/ \(2x\left(x+5\right)=\left(x+3\right)^2+\left(x-1\right)^2+20.\)
\(2x^2+10x=x^2+6x+9+x^2-2x+1+20.\)
\(10x=4x+30\)
\(6x=30\Rightarrow x=5\)
các câu còn lại tương tự
\(a,2x\left(x+5\right)=\left(x+3\right)^2+\left(x-1\right)^2+20\)
\(\Leftrightarrow2x^2+10x=x^2+6x+9+x^2-2x+1+20\)
\(\Leftrightarrow2x^2+10x=2x^2+4x+30\)
\(\Leftrightarrow2x^2+10x-2x^2-4x=30\)
\(\Leftrightarrow6x=30\)
\(\Leftrightarrow x=5\)
Vậy ...........
\(b,\left(2x-2\right)^2=\left(x+1\right)^2+3\left(x-2\right)\left(x+5\right)\)
\(\Leftrightarrow4x^2-8x+4=x^2+2x+1+3x^2+15x-6x-30\)
\(\Leftrightarrow4x^2-8x+4=4x^2+11x-29\)
\(\Leftrightarrow4x^2-8x-4x^2-11x=-29-4\)
\(\Leftrightarrow-19x=-33\)
\(\Leftrightarrow x=\frac{33}{19}\)
Vậy...........
\(c,\left(x-1\right)^2+\left(x+3\right)^2=2\left(x-2\right)\left(x+1\right)+38\)
\(\Leftrightarrow x^2-2x+1+x^2+6x+9=2x^2+2x-4x-4+38\)
\(\Leftrightarrow2x^2+4x+10=2x^2-2x+34\)
\(\Leftrightarrow2x^2+4x-2x^2+2x=34-10\)
\(\Leftrightarrow6x=24\)
\(\Leftrightarrow x=4\)
Vậy.............
\(d,\left(x+2\right)^3-\left(x-2\right)^3=12x\left(x-1\right)-18\)
\(\Leftrightarrow x^3+6x+12x+8-\left(x^3-6x+12x-8\right)=12x^2-12x-8\)
\(\Leftrightarrow x^3+6x+12x+8-x^3+6x-12x+8=12x^2-12x-8\)
\(\Leftrightarrow12x=-24\)
\(\Leftrightarrow x=-2\)
Vậy............
2.
\(\left(1+2+3+...+100\right)\cdot\left(1^2+2^2+3^2+...+10^2\right)\cdot\left(65\cdot111-13\cdot15\cdot37\right)\\ =\left(1+2+3+...+100\right)\cdot\left(1^2+2^2+3^2+...+10^2\right)\cdot\left(65\cdot111-13\cdot5\cdot3\cdot37\right)\\=\left(1+2+3+...+100\right)\cdot\left(1^2+2^2+3^2+...+10^2\right)\cdot\left[65\cdot111-\left(13\cdot5\right)\cdot\left(3\cdot37\right)\right]\\ =\left(1+2+3+...+100\right)\cdot\left(1^2+2^2+3^2+...+10^2\right)\cdot\left[65\cdot111-65\cdot111\right]\\ =\left(1+2+3+...+100\right)\cdot\left(1^2+2^2+3^2+...+10^2\right)\cdot0\\ =0\)
Lời giải:
$2^x+2^{x+2}+2^{x+2}=960-2^{x+3}$
$2^x+2^{x+2}+2^{x+2}+2^{x+3}=960$
$2^x(1+2^2+2^2+2^3)=960$
$2^x.17=960$
$2^x=960:17=56,4....$
Số khá xấu bạn xem lại nhé.