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Dài thế trời!!!

1) 1/3 x 1/2 x 3/7 = 1/6 x 3/7 = 1/14

2) 5/4 x 1/3 + 1/7 = 5/12 + 1/7 = 47/84

3) 8 x (8/9 - 2/3) = 8 x 2/9 = 16/9

4) 5/6 x 48/20 x 1/2 = 2 x 1/2 = 1

5) (2/5 + 3/4) x 8 = 23/20 x 8 = 46/5

6) 10 x (1/2 - 1/5) = 10 x 3/10 = 3

1x2= 2       1x2x3=6             1x2x3x4=24               1x2x3x4x5=120            1x2x3x4x5x6=720                   1x2x3x4x5x6x7=5040 

1x2x3x4x5x6x7x8=40320                 1x2x3x4x5x6x7x8x9=362880           1x2x3x4x5x6x7x8x9x10=3628800

1 x 2 = 2

1 x 2 x 3 = 6

1 x 2 x 3 x 4 = 24

1 x 2 x 3 x 4 x 5 = 120

1 x 2 x 3 x 4 x 5 x 6 = 720

1 x 2 x 3 x 4 x 5 x 6 x 7 = 5040

1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 = 40320

1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 = 362880

1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 = 3628800

a) \(x-\dfrac{3}{4}=6\times\dfrac{3}{8}\)

\(x-\dfrac{3}{4}=\dfrac{9}{4}\)

=> \(x=\dfrac{9}{4}+\dfrac{3}{4}=3\)

b) \(\dfrac{7}{8}:x=3-\dfrac{1}{2}\)

\(\dfrac{7}{8}:x=\dfrac{5}{2}\)

=> \(x=\dfrac{7}{8}:\dfrac{5}{2}=\dfrac{7}{20}\)

c) \(x+\dfrac{1}{2}\times\dfrac{1}{3}=\dfrac{3}{4}\)

\(x+\dfrac{1}{6}=\dfrac{3}{4}\)

=> \(x=\dfrac{3}{4}-\dfrac{1}{6}=\dfrac{7}{12}\)

d) \(\dfrac{3}{2}\times\dfrac{4}{5}-x=\dfrac{2}{3}\)

\(\dfrac{6}{5}-x=\dfrac{2}{3}\)

=> \(x=\dfrac{6}{5}-\dfrac{2}{3}=\dfrac{8}{15}\)

e) \(x\times3\dfrac{1}{3}=3\dfrac{1}{3}:4\dfrac{1}{4}\)(?)

\(x\times\dfrac{10}{3}=\dfrac{40}{51}\)

=> \(x=\dfrac{40}{51}:\dfrac{10}{3}=\dfrac{4}{17}\)

f) \(5\dfrac{2}{3}:x=3\dfrac{2}{3}-2\)

\(\dfrac{17}{3}:x=\dfrac{5}{3}\)

=> \(x=\dfrac{17}{3}:\dfrac{5}{3}=\dfrac{17}{5}\)

a: =>x-3/4=18/8=9/4

=>x=9/4+3/4=12/4=3

b: =>7/8:x=5/2

=>x=7/8:5/2=7/8*2/5=14/40=7/20

c: x+1/2*1/3=3/4

=>x+1/6=3/4

=>x=3/4-1/6=9/12-2/12=7/12

d: =>12/10-x=2/3

=>6/5-x=2/3

=>x=6/5-2/3=18/15-10/15=8/15

e: =>x*10/3=10/3:17/4=10/3*4/17

=>x=4/17

f: =>17/3:x=13/3-5/2=26/6-15/6=11/6

=>x=17/3:11/6=17/3*6/11=34/11

8 x 1 = 8        8 x 2 = 16       8 x 3 = 24       8 x 4 = 32

1 x 8 = 8        2 x 8 = 16       3 x 8 = 24       4 x 8 = 32

8 x 5 = 40       8 x 6 = 48       8 x 7 = 56       8 x 8 = 64

5 x 8 = 40       6 x 8 = 48       7 x 8 = 56       8 x 9 = 72

\(a,\dfrac{-1}{8}=\dfrac{3}{x}\\ \dfrac{3}{-24}=\dfrac{3}{x}\\ x=-24\\ b,\dfrac{x}{3}=\dfrac{3}{x}\\ x.x=3.3\\ x^2=9\\ x=\pm3\\ c,\dfrac{3}{4}.x=1\dfrac{1}{2}\\ \dfrac{3}{4}.x=\dfrac{3}{2}\\ x=\dfrac{3}{2}:\dfrac{3}{4}\\ x=2\\ d,x-\dfrac{3}{10}=\dfrac{7}{15}:\dfrac{3}{5}\\ x-\dfrac{3}{10}=\dfrac{7}{9}\\ x=\dfrac{7}{9}+\dfrac{3}{10}\\ x=\dfrac{97}{90}\\ e,\dfrac{-4}{7}-x=\dfrac{-8}{3}.\dfrac{3}{7}\\ \dfrac{-4}{7}-x=\dfrac{-8}{7}\\ x=\dfrac{-4}{7}+\dfrac{8}{7}\\ x=\dfrac{4}{7}\\ \)

fan liver tốt ghê

Cảm ơn nhe.^_^

1, \(45+x^3-5x^2-9x=9\left(5-x\right)+x^2\left(x-5\right)\)

\(=\left(9-x^2\right)\left(x-5\right)=\left(3-x\right)\left(x+3\right)\left(x-5\right)\)

3, \(x^4-5x^2+4\)

Đặt \(x^2=t\left(t\ge0\right)\)ta có : 

\(t^2-5t+4=t^2-t-4t+4=t\left(t-1\right)-4\left(t-1\right)\)

\(=\left(t-4\right)\left(t-1\right)=\left(x^2-4\right)\left(x^2-1\right)=\left(x-2\right)\left(x+2\right)\left(x-1\right)\left(x+1\right)\)

`Answer:`

1. `45+x^3-5x^2-9x`

`=x^3+3x^2-8x^2-24x+15x+45x`

`=x^2 .(x+3)-8x.(x+3)+15.(x+3)`

`=(x+3).(x^2-8x+15)`

`=(x+3).(x^2-5x-3x+15)`

`=(x-3).(x-5).(x-3)`

2. `x^4-2x^3-2x^2-2x-3`

`=x^4+x^3-3x^3+x^2+x-3x-3`

`=x^3 .(x+1)-3x^2 .(x+1)+x.(x+1)-3.(x+1)`

`=(x+1).(x^3-3x^2+x-3)`

`=(x+1).[x^3 .(x-3).(x-3)]`

`=(x+1).(x-3).(x^2+1)`

3. `x^4-5x^2+4`

`=x^4-x^2-4x^2+4`

`=x^2 .(x^2-1)-4.(x^2-1)`

`=(x^2-1).(x^2-4)`

`=(x-1).(x+1).(x-2).(x+2)`

4. `x^4+64`

`=x^4+16x^2+64-16x^2`

`=(x^2+8)^2-16x^2`

`=(x^2+8-4x).(x^2+8+4x)`

5. `x^5+x^4+1`

`=x^5+x^4+x^3-x^3+1`

`=x^3 .(x^2+x+1)-(x^3-1)`

`=x^3 .(x^2+x+1)-(x-1).(x^2+x+1)`

`=(x^2+x+1).(x^3-x+1)`

6. `(x^2+2x).(x^2+2x+4)+3`

`=(x^2+2x)^2+4.(x^2+2x)+3`

`=(x^2+2x)^2+x^2+2x+3.(x^2+2x)+3`

`=(x^2+2x+1).(x^2+2x)+3.(x^2+2x+1)`

`=(x^2+2x+1).(x^2+2x+3)`

`=(x+1)^2 .(x^2+2x+3)`

7. `(x^3+4x+8)^2+3x.(x^2+4x+8)+2x^2`

`=x^6+8x^4+16x^3+16x^2+64x+64+3x^3+12x^2+24x+2x^2`

`=x^6+8x^4+19x^3+30x^2+88x+64`

8. `x^3 .(x^2-7)^2-36x`

`=x[x^2.(x^2-7)^2-36]`

`=x[(x^3-7x)^2-6^2]`

`=x.(x^3-7x-6).(x^3-7x+6)`

`=x.(x^3-6x-x-6).(x^3-x-6x+6)`

`=x.[x.(x^2-1)-6.(x+1)].[x.(x^2-1)-6.(x-1)]`

`=x.(x+1).[x.(x-1)-6].(x-1).[x.(x+1)-6]`

`=x.(x+1).(x-1).(x^2-3x+2x-6).(x^2+3x-2x-6)`

`=x.(x+1).(x-1).[x.(x-3)+2.(x-3)].[x.(x+3)-2.(x+3)]`

`=x.(x+1)(x-1).(x-2).(x+2).(x-3).(x+3)`

9. `x^5+x+1`

`=x^5-x^2+x^2+x+1`

`=x^2 .(x^3-1)+(x^2+x+1)`

`=x^2 .(x-1).(x^2+x+1)+(x^2+x+1)`

`=(x^2+x+1).(x^3-x^2+1)`

10. `x^8+x^4+1`

`=[(x^4)^2+2x^4+1]-x^4`

`=(x^4+1)^2-(x^2)^2`

`=(x^4-x^2+1).(x^4+x^2+1)`

`=[(x^4+2x^2+1)-x^2].(x^4-x^2+1)`

`=[(x^2+1)^2-x^2].(x^4-x^2+1)`

`=(x^2-x+1).(x^2+x+1).(x^4-x^2+1)

11. ` x^5-x^4-x^3-x^2-x-2`

`=x^5-2x^4+x^4-2x^3+x^3-2x^2+x^2-2x+x-2`

`=x^4 .(x-2)+x^3 ,(x-2)+x^2 .(x-2)+x.(x-2)+(x-2)`

`=(x-2).(x^4+x^3+x^2+x+1)`

12. `x^9-x^7-x^6-x^5+x^4+x^3+x^2-1`

`=(x^9-x^7)-(x^6-x^4)-(x^5-x^3)+(x^2-1)`

`=x^7 .(x^2-1)-x^4 .(x^2-1)-x^3 .(x^2-1)+(x^2-1)`

`=(x^2-1).(x^7-x^4-x^3+1)`

`=(x-1)(x+1)(x^3-1)(x^4-1)`

`=(x-1)(x+1)(x^2+x+1)(x-1)(x^2-1)(x^2+1)`

`=(x-1)^2 .(x+1)(x^2+x+1)(x-1)(x+1)(x^2+1)`

`=(x-1)^3 .(x+1)^2 .(x^2+x+1)(x^2+1)`

13. `(x^2-x)^2-12(x^2-x)+24`

`=[ (x^2-x)^2-2.6(x^2-x)+6^2]-12`

`=(x^2-x+6)^2-12`

`=(x^2-x+6-\sqrt{12})(x^2-x+6+\sqrt{12})`

1: x=3/4-1/2=3/4-2/4=1/4

2: x-1/5=2/11

=>x=2/11+1/5=21/55

3: x-5/6=16/42-8/56

=>x-5/6=8/21-4/28=5/21

=>x=5/21+5/6=15/14

4: x/5=5/6-19/30

=>x/5=25/30-19/30=6/30=1/5

=>x=1

5: =>|x|=1/3+1/4=7/12

=>x=7/12 hoặc x=-7/12

6: x=-1/2+3/4

=>x=3/4-1/2=1/4

11: x-(-6/12)=9/48

=>x+1/2=3/16

=>x=3/16-1/2=-5/16

1)x= 1/4

2)x= 2/11+ 1/5

   x= 21/55

3)x - 5/6 = 5/21

   x         = 5/21+5/6

   x         = 15/14

4)x/5 = 5/6 + -19/30

   x:5 = 1/5

   x    = 1/5.5

   x    = 1

5) |x| - 1/4 = 6/18

    |x|           = 6/18 - 1/4

    |x|            =7/12

⇒x= 7/12 hoặc -7/12

6)x = -1/2 +3/4

   x= 1/4

7) x/15 = 3/5 + -2/3

   x:15  = -1/15

  x        = -1/15. 15

  x        = -1

8)11/8 + 13/6 = 85/x  

       85/24      = 85/x

  ⇒      x           = 24

9) x - 7/8 = 13/12

   x          = 13/12 + 7/8

   x          = 47/24

10)x - -6/15 = 4/27  

     x            = 4/27 + (-6/15)

    x             = -34/135

11) -(-6/12)+x = 9/48

                    x= 9/48 - 6/12

                    x = -5/16

12) x - 4/6 = 5/25 + -7/15

      x -4/6  =  -4/15

     x           = -4/15 + 4/6

    x             = 2/5

`(x - 2)/3 = (x + 1)/4`

`(x - 2) . 4 = (x + 1) . 3`

`<=> 4x - 8 = 3x + 3`

`<=> 4x - 3x = 3 + 8`

`<=> (4 - 3)x = 11`

`=> x = 11`

`=>` `x = 11`

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