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:>?

\(\frac{3}{3.6.9}+\frac{3}{6.9.12}+\frac{3}{9.12.15}+\frac{3}{12.15.18}=\frac{3}{6}\left(\frac{6}{3.6.9}+\frac{6}{6.9.12}+\frac{6}{9.12.15}+\frac{6}{12.15.18}\right)\)

= \(\frac{1}{2}\left(\frac{1}{3.6}-\frac{1}{6.9}+\frac{1}{6.9}-\frac{1}{9.12}+\frac{1}{9.12}-\frac{1}{12.15}+\frac{1}{12.15}-\frac{1}{15.18}\right)\)

\(=\frac{1}{2}\left(\frac{1}{3.6}-\frac{1}{15.18}\right)=\frac{1}{2}.\frac{14}{270}=\frac{7}{270}\)

a) 6 . x - 15 = 15

6 . x = 15 + 15

6 . x = 30

x = 30 : 6

x = 5

b) 2 . x + 3 = 9

2 . x = 9 - 3

2 . x = 6

x = 6 : 2

x = 3

c) 17 - 6 : x = 15

6 : x = 17 - 15

6 : x = 2

x = 6 : 2

x = 3

d) x : 3 + 12 = 14

x : 3 = 14 - 12

x : 3 = 2

x = 2 . 3

x = 6

a) 6 . x -15 = 15 

⇒ 6 .x = 15 + (-15)

⇒ 6 .x = 0

⇔ x = 0

Vậy x = 0.

Áp dụng bất đẳng thức AM - GM:

\(\sqrt{\left(x^2-15\right)\left(x-3\right)}\le\dfrac{x^2-15+x-3}{2}=\dfrac{x^2+x-18}{2};\sqrt{x^2-15}\le\dfrac{x^2-15+1}{2}=\dfrac{x^2-14}{2};\sqrt{x-3}\le\dfrac{x-3+1}{2}=\dfrac{x-2}{2}\).

Do đó \(F\ge x^2+x-\dfrac{x^2+x-18}{2}-\dfrac{x^2-14}{2}-\dfrac{x-2}{2}-38=-21\).

Đẳng thức xảy ra khi x = 4.

Vậy...

x=-36

x=11

x=100

x=14

x=-36

x=11

x=100

x=14

1: =>3^x=81

=>x=4

2: =>2^x=8

=>x=3

3: =>x^3=2^3

=>x=2

4: =>x^20-x=0

=>x(x^19-1)=0

=>x=0 hoặc x=1

5: =>2^x=32

=>x=5

6: =>(2x+1)^3=9^3

=>2x+1=9

=>2x=8

=>x=4

7: =>x^3=115

=>\(x=\sqrt[3]{115}\)

8: =>(2x-15)^5-(2x-15)^3=0

=>(2x-15)^3*[(2x-15)^2-1]=0

=>2x-15=0 hoặc (2x-15)^2-1=0

=>2x-15=0 hoặc 2x-15=1 hoặc 2x-15=-1

=>x=15/2 hoặc x=8 hoặc x=7

1. Tìm số tự nhiên x biết:

1) \(3^x.3=243\)

\(3^x=243:3\)

\(3^x=81\)

\(3^x=3^4\)

\(\Rightarrow x=4\)

_____

2) \(7.2^x=56\)

\(2^x=56:7\)

\(2^x=8\)

\(2^x=2^3\)

\(\Rightarrow x=3\)

_____

3) \(x^3=8\)

\(x^3=2^3\)

\(\Rightarrow x=3\)

_____

4) \(x^{20}=x\)

\(x^{20}-x=0\)

\(x\left(x^{19}-1\right)=0\)

\(\Rightarrow x=0\) hoặc \(x=1\)

5) \(2^x-15=17\)

\(2^x=17+15\)

\(2^x=32\)

\(2^x=2^5\)

\(\Rightarrow x=5\)

_____

6) \(\left(2x+1\right)^3=9.81\)

\(\left(2x+1\right)^3=729=9^3\)

\(\rightarrow2x+1=9\)

\(2x=9-1\)

\(2x=8\)

\(x=8:2\)

\(\Rightarrow x=4\)

_____

7) \(x^6:x^3=125\)

\(x^3=125\)

\(x^3=5^3\)

\(\Rightarrow x=5\)

_____

8) \(\left(2x-15\right)^5=\left(2x-15\right)^3\)

\(\rightarrow\left(2x-15\right)^5-\left(2x-15\right)^3=0\)

\(\left(2x-15\right)^3.\left[\left(2x-15\right)^2-1\right]=0\)

\(\Leftrightarrow\left\{{}\begin{matrix}\left(2x-15\right)^3=0\\\left(2x-15\right)^2-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{15}{2}\\x=7\\x=8\end{matrix}\right.\)

_____

9) \(3^{x+2}-5.3^x=36\)

\(3^x.\left(3^2-5\right)=36\)

\(3^x.\left(9-5\right)=36\)

\(3^x.4=36\)

\(3^x=36:4\)

\(3^x=9\)

\(3^x=3^2\)

\(\Rightarrow x=2\)

_____

10) \(7.4^{x-1}+4^{x+1}=23\)

\(\rightarrow7.4^{x-1}+4^{x-1}.4^2=23\)

\(4^{x-1}.\left(7+4^2\right)=23\)

\(4^{x-1}.\left(7+16\right)=23\)

\(4^{x-1}.23=23\)

\(4^{x-1}=23:23\)

\(4^{x-1}=1\)

\(4^{x-1}=4^1\)

\(\rightarrow x-1=0\)

\(x=0+1\)

\(\Rightarrow x=1\)

Chúc bạn học tốt

d, x=-110

\(a,3\left(x-5\right)-4\left(x-3\right)=-12\)

\(\Leftrightarrow3x-15-4x+12=-12\)

\(\Leftrightarrow-x=-9\)

\(\Leftrightarrow x=9\)

Vậy x=9

75 nhé bạn

TL :

   ( 15 x 15 ) : 2 x ( 15 x 15 ) : 2 x ( 15 x 15 ) : 2 + ( 0 + 1 + 2 + 2 + 3 + 45 ) x 0

= 0

=> vì : tất cả số nào nhân vs 0 đều = 0

_HT_

Đặt A=1 / 1 x 3 + 2 / 3 x 7 + 1 / 7 x 9 + 3 / 9 x 15 + 6 / 15 x 27 

2A=2 / 1 x 3 + 4 / 3 x 7 + 2 / 7 x 9 + 6 / 9 x 15 + 12 / 15 x 27 

2A=1-1/3+1/3-1/7+1/7-1/9+1/9-1/15+1/15-1/27

2A=1-1/27

2A=26/27

A=13/27

`@` `\text {Ans}`

`\downarrow`

`a)`

`x + 10 = 20`

`=> x = 20 -10`

`=> x = 10`

Vậy, `x = 10`

`b)`

`2 * x + 15 = 35`

`=> 2x = 35 - 15`

`=> 2x = 20`

`=> x = 20 \div 2`

`=> x = 10`

Vậy, `x = 10`

`c)`

`3 * ( x + 2 ) = 15`

`=> x + 2 = 15 \div 3`

`=> x + 2 = 5`

`=> x = 5 - 2`

`=> x = 3`

Vậy, `x = 3`

`d)`

`10 * x + 15 * 11 = 20 * 10`

`=> 10x + 165 = 200`

`=> 10x = 200 - 165`

`=> 10x = 35`

`=> x = 35 \div 10`

`=> x = 3,5`

Vậy,` x = 3,5`

`e)`

`4 * ( x + 2 ) = 3 * 4`

`=> x + 2 = 12 \div 4`

`=> x + 2 = 3`

`=> x = 3 - 2`

`=> x = 1`

Vậy,` x = 1`

`f)`

`33 x + 135 = 26 * 9`

`=> 33x + 135 = 234`

`=> 33x = 234 - 135`

`=> 33x = 99`

`=> x = 99 \div 33`

`=> x = 3`

Vậy, `x = 3`

`g)`

`2 * x + 15 + 16 + 17 = 100`

`=> 2x + 48 = 100`

`=> 2x = 100 - 48`

`=> 2x = 52`

`=> x = 52 \div 2`

`=> x =26`

`h)`

`2 * (x + 9 + 10 + 11) = 4 . 12 . 25`

`=> 2 * (x + 9 + 10 + 11) = 4*25*12`

`=> 2 * (x + 9 + 10 + 11) = 100*12`

`=> x + 9 + 10 + 11 = 100*12 \div 2`

`=> x + 30 = 600`

`=> x = 600 - 30`

`=> x = 570`

Vậy, `x = 570.`

a) \(x+10=20\Leftrightarrow x=10\)

b) \(2x+15=35\Leftrightarrow2x=20\Leftrightarrow x=10\)

c) \(3.\left(x+2\right)=15\Leftrightarrow x+2=5\Leftrightarrow x=3\)

d) \(10x+15.11=20.10\Leftrightarrow10x+165=200\Leftrightarrow10x=35\Leftrightarrow x=\dfrac{35}{10}=\dfrac{7}{2}\)

e) \(4.\left(x+2\right)=3.4\Leftrightarrow x+2=3\Leftrightarrow x=1\)

f) \(35x+135=26.9\Leftrightarrow35x=234-135\Leftrightarrow35x=99\Leftrightarrow x=\dfrac{99}{35}\)

g) \(2x+15+16+17=100\Leftrightarrow2x+48=100\Leftrightarrow2x=52\Leftrightarrow x=26\)

h) \(2.\left(x+9+10+11\right)=4.12.25\)

\(\Leftrightarrow x+30=2.12.25\)

\(\Leftrightarrow x=600-30\)

\(\Leftrightarrow x=570\)