Bài 1:

\(x\) \(\times\) \(\dfrac{15}{16}\) - \(x\) \(\times\) \(\dfrac{4}{16}\) = 2

\(x\) \(\times\) (\(\dfrac{15}{16}\) - \(\dfrac{4}{16}\)) = 2

\(x\) \(\times\) \(\dfrac{11}{16}\) = 2

\(x\) = 2 : \(\dfrac{11}{16}\)

\(x\) = 2 x \(\dfrac{16}{11}\)

\(x\) = \(\dfrac{32}{11}\)

Bài 2: 1 + \(\dfrac{1}{3}\) + \(\dfrac{1}{6}\) + \(\dfrac{1}{10}\) + ... + \(\dfrac{1}{x\left(x+1\right):2}\) = 1 : \(\dfrac{2011}{2012}\)

1 + 2\(\times\) ( \(\dfrac{1}{2\times3}\) + \(\dfrac{1}{2\times6}\) + \(\dfrac{1}{2\times10}\) + ... + \(\dfrac{2}{2\times x\times\left(x+1\right)}\)) = \(\dfrac{2012}{2011}\)

1 + 2 \(\times\)(\(\dfrac{1}{2\times3}\) + \(\dfrac{1}{12}\) + \(\dfrac{1}{20}\)+...+ \(\dfrac{1}{x\times\left(x+1\right)}\)) = \(\dfrac{2012}{2011}\)

1 + 2 \(\times\) (\(\dfrac{1}{2\times3}\) + \(\dfrac{1}{3\times4}\) + ... + \(\dfrac{1}{x\times\left(x+1\right)}\)) = 1 + \(\dfrac{1}{2011}\)

1 + 2\(\times\)(\(\dfrac{1}{2}\) - \(\dfrac{1}{3}\) + \(\dfrac{1}{3}\) - \(\dfrac{1}{4}\) + ... + \(\dfrac{1}{x}\) - \(\dfrac{1}{x+1}\)) = 1 + \(\dfrac{1}{2011}\)

 1 + 2 \(\times\) (\(\dfrac{1}{2}\) - \(\dfrac{1}{x+1}\)) = 1 + \(\dfrac{1}{2011}\)

  1 + 1 - \(\dfrac{2}{x+1}\) = 1 + \(\dfrac{1}{2011}\)

    \(\dfrac{2}{x+1}\) = 1 + 1 - 1  - \(\dfrac{1}{2011}\)

    \(\dfrac{2}{x+1}\) =  2 - 1 - \(\dfrac{1}{2011}\)

  \(\dfrac{2}{x+1}\)  = 1 - \(\dfrac{1}{2011}\)

     \(\dfrac{2}{x+1}\) = \(\dfrac{2010}{2011}\)

       \(x\) + 1 = 2 : \(\dfrac{2010}{2011}\)

        \(x\) + 1 = \(\dfrac{2011}{1005}\)

         \(x\) = \(\dfrac{2011}{1005}\) - 1  = \(\dfrac{1006}{1005}\)(loại vì \(\dfrac{1006}{1005}\) không phải là số tự nhiên)

Vậy không có giá trị nào của \(x\) là số tự nhiên thỏa mãn đề bài. 

Bài 3:

\(\dfrac{x}{16}\) \(\times\) (2017 - 1) = 2

\(\dfrac{x}{16}\) \(\times\) 2016 = 2

 \(\dfrac{x}{16}\)             = 2 : 2016

 \(\dfrac{x}{16}\)            = \(\dfrac{1}{1008}\)

   \(x\)             = \(\dfrac{1}{1008}\) x 16

  \(x\) = \(\dfrac{1}{63}\)

\(4x-\left(x+\frac{1}{2}\right)=2x-\left(\frac{1}{2}-5\right)\)

\(4x-x-\frac{1}{2}=2x-\frac{1}{2}+5\)

\(3x-\frac{1}{2}=2x-\frac{1}{2}+5\)

\(3x-\frac{1}{2}-2x-\frac{1}{2}+5=0\)

\(3x-2x-\frac{1}{2}-\frac{1}{2}+5=0\)

\(x-0+5=0\)

\(x+5=0\)

\(x=0-5=-5\)

x+1/2+x+1/8+x+1/16=1

(x+x+x)+(1/2+1/8+1/16)=1

3x+11/16=1

3x=1-11/16

3x=5/16

x=5/16:3

x=5/16x3

x=15/16

mk nhầm:

5/16:3=5/16x1/3=5/48

mong bạn thông cảm!

\(\left(x+\frac{1}{2}\right)+\left(x+\frac{1}{8}\right)+\left(x+\frac{1}{16}\right)=1\)

\(\Leftrightarrow\left(x+x+x\right)+\left(\frac{1}{2}+\frac{1}{8}+\frac{1}{16}\right)=1\)

\(\Leftrightarrow3x+\left(\frac{1}{2}+\frac{1}{8}+\frac{1}{16}\right)=1\)

\(\Leftrightarrow3x+\frac{11}{16}=1\)

\(3x=1-\frac{11}{16}\)

\(3x=\frac{5}{16}\)

\(x=\frac{5}{16}:3\)

\(x=\frac{5}{48}\)

1/2-(4/12+9/12)<x<1/24-(3/24-8/24)

1/2-13/12<x<1/24-(-5/24)

-7/12<x<1/4

=>x\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\) E{0}

ta có:\(\frac{1}{2}-\left(\frac{1}{3}+\frac{3}{4}\right)=\frac{-1}{12}=-0,08333333\)

mà \(\frac{1}{24}-\left(\frac{1}{8}-\frac{1}{3}\right)=\frac{1}{4}=0.25\)

nên suy ra không có số nguyên x nào thỏa mãn đề bài.

Sao ai cũng giải khó hiểu thế vậy trời:))

Bé Na tìm đây nha:

Câu hỏi của ngô thị gia linh - Toán lớp 6 - Học toán với OnlineMath

hay Giải toán trên mạng - Giúp tôi giải toán - Hỏi đáp, thảo luận về toán học - Học toán với OnlineMath

........

b) 9/5 : (2 . x + 1) - 2 = 7

9/5 : ( 2 . x + 1) = 7 + 2 

9/5 : ( 2 . x + 1) = 9

          2 . x + 1  = 9/5 : 9

          2 . x + 1   = 1/5

          2 . x          = 1/5 - 1 

           2 . x          = - 4/5

                x          = - 4/5 : 2 

                x          = - 2/5

b) 9/5 : (2 . x + 1) - 2 = 7

9/5 : ( 2 . x + 1) = 7 + 2 

9/5 : ( 2 . x + 1) = 9

          2 . x + 1  = 9/5 : 9

          2 . x + 1   = 1/5

          2 . x          = 1/5 - 1 

           2 . x          = - 4/5

                x          = - 4/5 : 2 

                x          = - 2/5

k cho mk nha

Ta có:

\(\left(\frac{1}{5}+\frac{1}{3}+\frac{3}{10}\right)+-\frac{1}{2}=\frac{1}{5}+\frac{1}{3}+\frac{3}{10}\)\(-\frac{1}{2}\)

=\(\frac{6}{30}+\frac{10}{30}+\frac{9}{30}-\frac{15}{30}=\frac{6+10+9-15}{30}=\frac{10}{30}=\frac{1}{3}\)

h: \(\left(-145\right)-5\left(2x-1\right)^3=480\)

=>\(5\left(2x-1\right)^3=-145-480\)=-625

=>(2x-1)³=-125

=>2x-1=-5

=>2x=-5+1=-4

=>x=-4/2=-2

k: \(3\left(-4+x\right)^3-\left(-4\right)^2=-97\)

=>\(3\left(x-4\right)^3-16=-97\)

=>\(3\cdot\left(x-4\right)^3=-97+16=-81\)

=>\(\left(x-4\right)^3=-27\)

=>x-4=-3

=>x=-3+4=1

n: \(195+3\left(-2x+5\right)^3=192\)

=>\(3\left(-2x+5\right)^3=192-195=-3\)

=>\(\left(-2x+5\right)^3=-1\)

=>-2x+5=-1

=>-2x=-1-5=-6

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

o: \(\left(-148\right)-5\left(-x+6\right)^4=-228\)

=>\(148+5\left(x-6\right)^4=228\)

=>\(5\left(x-6\right)^4=80\)

=>\(\left(x-6\right)^4=16\)

=>\(\left[{}\begin{matrix}x-6=2\\x-6=-2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=8\\x=4\end{matrix}\right.\)

p: \(-43-\left(-4+x\right)^4=-44\)

=>\(\left(x-4\right)^4+43=44\)

=>\(\left(x-4\right)^4=1\)

=>\(\left[{}\begin{matrix}x-4=1\\x-4=-1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=5\\x=3\end{matrix}\right.\)

q: \(3\left(-x+5\right)^2-\left(-5\right)^2\cdot\left(-2\right)^3=203\)

=>\(3\left(x-5\right)^2-25\cdot\left(-8\right)=203\)

=>\(3\left(x-5\right)^2+200=203\)

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

=>(x-5)²=1

=>\(\left[{}\begin{matrix}x-5=1\\x-5=-1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=6\\x=4\end{matrix}\right.\)

h.

$(-145)-5(2x-1)^3=480$

$5(2x-1)^3=-145-480=-625$

$(2x-1)^3=-625:5=-125=(-5)^3$

$\Rightarrow 2x-1=-5$

$\Rightarrow x=-3$

k.

$3(-4+x)^3-(-4)^2=-97$

$3(-4+x)^3-16=-97$

$3(-4+x)^3=-97+16=-81$

$(-4+x)^3=-81:3=-27=(-3)^3$

$\Rightarrow -4+x=-3$

$\Rightarrow x=-3-(-4)=1$

m. Không rõ đề.

n.

$195+3(-2x+5)^3=192$

$3(-2x+5)^3=192-195=-3$

$(-2x+5)^3=-3:3=-1=(-1)^3$

$\Rightarrow -2x+5=-1$

$\Rightarrow -2x=-6$

$\Rightarrow x=3$

khỏi cần chú ý người khác cũng biết ai ai mà chẳng biết

\(\left(1+\frac{1}{5}\right)\cdot\left(1+\frac{1}{6}\right)\cdot....+\left(1+\frac{1}{2014}\right)\)

=\(\frac{6}{5}\cdot\frac{7}{6}\cdot...\cdot\frac{2015}{2014}\)

=\(\frac{2015}{5}\)

=403