a. x^2.y^2=162

ta có \(\frac{x}{2}=\frac{y}{1}=\frac{z}{3}\)=>\(\frac{x^2}{4}=\frac{y^2}{1}=\frac{z^2}{9}\)

=>\(\frac{x^2}{4}.\frac{y^2}{1}=\frac{z^4}{81}\)còn lại do đề sai :))

b.\(\frac{2x}{3}=\frac{3y}{4}=\frac{z}{5}\)

=>\(\frac{x}{\frac{3}{2}}=\frac{y}{\frac{4}{3}}=\frac{z}{5}=\frac{x-y+z}{....}=\frac{26}{....}\)nhân phân phối là xong :))

a/ Dễ thấy x, y, z cùng dấu

\(\Rightarrow xy=\sqrt{162}=9\sqrt{2}\)

Ta lại có:

\(\frac{x}{2}.\frac{y}{1}=\frac{z^2}{9}\)

\(\Leftrightarrow z^2=\frac{9.9\sqrt{2}}{2}=\frac{81\sqrt{2}}{2}\)

\(\Rightarrow z=\pm9\sqrt{\frac{\sqrt{2}}{2}}=\pm\frac{9}{\sqrt[4]{2}}\)

Thế z tìm được x, y

a) 467 + x = 877 – 162

467 + x = 715

x = 715 – 467

x = 248

b) x – 214 = 61 + 345

x – 214 = 406

x = 406 + 214

x = 620

c) x : 5 = 10 × 2

x : 5 = 20

x = 20 × 5

x = 100

d) x × 4 = 30 – 10

x × 4 = 20

x = 20 : 4

x = 5

3:

a: 3^x*3=243

=>3^x=81

=>x=4

b; 2^x*16^2=1024

=>2^x=4

=>x=2

c: 64*4^x=16^8

=>4^x=4^16/4^3=4^13

=>x=13

d: 2^x=16

=>2^x=2^4

=>x=4

Tách ?

`a, 70 -5.(x-3) =45`

`=> 5.(x-3)= 70-45`

`=> 5.(x-3)=25`

`=>x-3=25:5`

`=>x-3=5`

`=>x= 5+3`

`=>x=8`

______

`b,10 + 2.x = 4^5:4^3`

`=> 10 + 2.x = 4^(5-3)`

`=> 10 + 2.x =4^2=16`

`=> 2.x=16-10`

`=>2.x=6`

`=>x=6:2`

`=>x=3`

_____

`c,60-3.x-2=51`

`=>  60-3.x= 51+2`

`=> 60-3.x=53`

`=>3.x=60-53`

`=> 3.x= 7`

`=>x= 7/3`

____

`d, 4.x-20=2^5:2^3`

`=> 4.x-20=2^(5-3)`

`=> 4.x-20=2^2`

`=> 4.x= 4+20`

`=>4.x=24`

`=>x=24:4`

`=>x=6`

____

`2^x . 4=16`

`=> 2^x=16:4`

`=>2^x= 4`

`=>2^x=2^2`

`=>x=2`

____

`f, 3^x . 3=243`

`=>3^x=243:3`

`=> 3^x=81`

`=> 3^x=3^3`

`=>x=3`

_____

`g, 64. 4^x =16^8`

`=> 4^3 . 4^x=(4^2)^8`

`=> 4^3 . 4^x = 4^(16)`

`=> 4^x= 4^(16-3)`

`=>4^x=4^(13)`

`=>x=13`

_____

`2^x . 16^2 =1024`

`=> 2^x= 1024 : 16^2`

`=>2^x=4`

`=>2^x=2^2`

`=>x=2`

a: =>5(x-3)=25

=>x-3=5

=>x=8

b: =>2x=16-10=6

=>x=3

c: =>58-3x=51

=>3x=7

=>x=7/3

d: =>4x-20=4

=>4x=24

=>x=6

e: =>2^x=4

=>2^x=2^2

=>x=2

f: =>3^x=81

=>3^x=3^4

=>x=4

g: =>4^x*4^3=4^16

=>x+3=16

=>x=13

h: =>2^x=1024/256=4=2^2

=>x=2

sai

a) \(\left|x+1\right|+\left|-13\right|=26\)

\(\left|x+1\right|+13=26\)

\(\left|x+1\right|=26-13\)

\(\left|x+1\right|=13\)

\(\Rightarrow\orbr{\begin{cases}x+1=13\\x+1=-13\end{cases}}\Rightarrow\orbr{\begin{cases}x=12\\x=-14\end{cases}}\)

vậy ........

b) \(3^{x+2}+3^x=250\)

\(3^x.3^2+3^x=250\)

\(3^x.\left(3^2+1\right)=250\)

\(3^x.10=250\)

\(3^x=25\)

\(\Rightarrow x\in\varnothing\) 

Những câu sau tương tự

\(\Leftrightarrow\left(x+2\right)\left(x^2-2x+2^2\right)-x\left(x^2-3^2\right)=26\\ \Leftrightarrow x^3+2^3-x^3+9x=26\\ \Leftrightarrow9x+8=26\\ \Rightarrow x=\dfrac{26-8}{9}=2\)

Lời giải:

$(x+2)(x^2-2x+4)-x(x+3)(x-3)=26$

$\Leftrightarrow x^3+8-x(x^2-9)=26$

$\Leftrightarrow 9x+8=26$

$\Leftrightarrow 9x=18$

$\Leftrightarrow x=2$

b, 2 + 4 + 6 +.....+2x =210

    =>2*(1+2+3+....+x) =210

  => 1+2+3+....+x = 105

   => (x+1)*x : 2 = 105

   => (x+1)*x  = 210

   => (x+1)*x  = 15*14

=>x=14

c) [(x  - 300)^2 - 280 ] * 2 = 19440

           => (x  - 300)^2 - 280  = 9720

           => (x  - 300)^2   = 10000 =100²

           => x  - 300 =100

=> x=400

a, 3^x-1+ 5* 3^x-1 = 162

             3^x-1 * (5 + 1) = 162

                    3^x-1 * 6 = 162

                               3^x-1  = 27 = 3³

                                   => x-1=3

                                            => x=4

321 x 3 + 321 x 5 + 321 x 2

= 321 x (3 + 5 + 2)

= 321 x 10

= 3 210.

321 x 3 + 321 x 5 + 321 x 2

= 321 x (3 + 5 + 2)

= 321 x 10

= 3210