=>(x-6)^4+(x-8)^4=16

Đặt a=x-7

=>(a-1)^4+(a+1)^4=16

=>a^4+4a^3+6a^2+4a+1+a^4-4a^3+6a^2-4a+1=16

=>2a^4+12a^2-14=0

=>a^4+6a^2-7=0

=>(a^2+7)(a^2-1)=0

=>a^2=1

=>a=1 hoặc a=-1

=>x-7=1 hoặc x-7=-1

=>x=6 hoặc x=8

Đặt \(t=x-7\)

Thay t vào phương trình ban đầu ta có: 

\(\left(t+1\right)^4+\left(t-1\right)^4=16\)

\(\left(t^4+4t^3+6t^2+4t+1\right)-\left(t^4-4t^3+6t^2-4t+1\right)=16\)

\(8t^3+8t=16\)

\(t^3+t-2=0\)

\(t=1\)

=> \(x-7=1\)

=> x = 8

Vậy x = 8 là giá trị cần tìm 

a) x × 5 = 35 – 5

x × 5 = 30

x = 30 : 5

x = 6

b) x : 4 = 12 – 8

x : 4 = 4

x = 4 × 4

x = 16

c) 4 × x = 6 × 2

4 × x = 12

x = 12 : 4

x = 3

d) x : 3 = 16 : 4

x : 3 = 4

x = 4 × 3

x = 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

a, 2^x=8^4/16^3 

<=> 2^x = (2^3)^4 / (2^4)^3

<=> 2^x = 2^12 / 2^12

<=> 2^x = 1

<=> 2^x = 2^0

<=> x = 0

Vậy x = 0

 b,2^x=2^6/4^3

<=> 2^x = 2^6 / (2^2)^3

<=> 2^x = 2^6 / 2^6

<=> 2^x = 1

<=> 2^x = 2^0

<=> x = 0

Vậy x = 0

Ta có: \(\frac{-6}{8}=\frac{x}{16}\Rightarrow x=\frac{16.\left(-6\right)}{8}=-12\)

Thế x = -12 \(\Rightarrow\frac{-12}{16}=\frac{-30}{y}\Rightarrow y=\frac{16.\left(-30\right)}{-12}=40\)

Thế y = 40 \(\Rightarrow\frac{-30}{40}=\frac{z}{-4}\Rightarrow z=\frac{\left(-30\right)\left(-4\right)}{40}=3\)

Vậy x = -12 ; y = 40, z = 3

1: \(\Leftrightarrow x=UCLN\left(24;36;150\right)=6\)

2: \(\Leftrightarrow x\in\left\{24;48;72;...\right\}\)

mà 16<=x<=50

nên \(x\in\left\{24;48\right\}\)

3: \(\Leftrightarrow x\inƯ\left(6\right)\)

mà x>-10

nên \(x\in\left\{1;-1;2;-2;3;-3;6;-6\right\}\)

4: \(\Leftrightarrow x\in BC\left(4;5;8\right)\)

\(\Leftrightarrow x\in\left\{...;-40;0;40;80;120;160;200;...\right\}\)

mà -20<x<180

nên \(x\in\left\{0;40;80;120;160\right\}\)