1:

a: \(=\dfrac{-4}{7}+\dfrac{4}{7}+\dfrac{3}{7}-\dfrac{23}{34}-\dfrac{4}{5}=\dfrac{3}{7}-\dfrac{23}{34}-\dfrac{4}{5}=-\dfrac{1247}{1190}\)

b:

Sửa đề: \(\dfrac{-5}{13}+\dfrac{4}{19}+\dfrac{-8}{13}+\dfrac{15}{19}+\dfrac{45}{6}\) 

\(=\dfrac{-5}{13}-\dfrac{8}{13}+\dfrac{4}{19}+\dfrac{15}{19}+\dfrac{45}{6}=\dfrac{9}{2}\)

\(a)x\times\dfrac{4}{7}=8\)                        \(b)\dfrac{1}{6}:x=\dfrac{5}{18}\)

\(x=8:\dfrac{4}{7}\)                                \(x=\dfrac{1}{6}:\dfrac{5}{18}\)

\(x=\dfrac{56}{4}=14\)                            \(x=\dfrac{18}{30}=\dfrac{3}{5}\)

a) x = 8 : 4/7

x = 14

b) x = 1/6 : 5/18

x = 3/5

3/5

b) \(2020^{x\left(x+6\right)}=1\)

\(\Leftrightarrow2020^{x\left(x+6\right)}=2020^0\)

\(\Leftrightarrow x\left(x+6\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x=0\\x+6=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=0\\x=-6\end{cases}}\)

Vậy \(x=0\)hoặc \(x=-6\)

a; \(\dfrac{2}{3}\)\(x\) - \(\dfrac{3}{2}\)\(x\) = \(\dfrac{5}{12}\)

    (\(\dfrac{2}{3}\) - \(\dfrac{3}{2}\))\(x\) = \(\dfrac{5}{12}\)

     - \(\dfrac{5}{6}\)\(x\) = \(\dfrac{5}{12}\)

     \(x\)   = \(\dfrac{5}{12}\) : (- \(\dfrac{5}{6}\))

     \(x=\) - \(\dfrac{1}{2}\)

Vậy \(x=-\dfrac{1}{2}\) 

b; \(\dfrac{2}{5}\) + \(\dfrac{3}{5}\).(3\(x\) - 3,7) = \(\dfrac{-53}{10}\)

           \(\dfrac{3}{5}\).(3\(x\) - 3,7) = \(\dfrac{-53}{10}\) - \(\dfrac{2}{5}\)

          \(\dfrac{3}{5}\).(3\(x\) - 3,7) = - \(\dfrac{57}{10}\)

         3\(x\) - 3,7 = - \(\dfrac{57}{10}\) : \(\dfrac{3}{5}\)

         3\(x\)   - 3,7 = - \(\dfrac{19}{2}\)

         3\(x\)         = - \(\dfrac{19}{2}\) + 3,7

          3\(x\)        = - \(\dfrac{29}{5}\)

           \(x\)         = - \(\dfrac{29}{5}\) : 3

           \(x\)        = - \(\dfrac{29}{15}\)

Vậy \(x\) \(\in\) - \(\dfrac{29}{15}\) 

c; \(\dfrac{7}{9}\) : (2 + \(\dfrac{3}{4}\)\(x\)) + \(\dfrac{5}{9}\) = \(\dfrac{23}{27}\)

    \(\dfrac{7}{9}\): (2 + \(\dfrac{3}{4}\)\(x\)) = \(\dfrac{23}{27}\) - \(\dfrac{5}{9}\)

     \(\dfrac{7}{9}\):(2 + \(\dfrac{3}{4}\)\(x\)) = \(\dfrac{8}{27}\)

      2 + \(\dfrac{3}{4}\)\(x\) = \(\dfrac{7}{9}\) : \(\dfrac{8}{27}\)

      2 + \(\dfrac{3}{4}\)\(x\) =  \(\dfrac{21}{8}\)

             \(\dfrac{3}{4}x\) = \(\dfrac{21}{8}\) - 2

             \(\dfrac{3}{4}\)\(x\) =  \(\dfrac{5}{8}\)

               \(x\) = \(\dfrac{5}{8}\) : \(\dfrac{3}{4}\)

              \(x\) =  \(\dfrac{5}{6}\)

Vậy \(x=\dfrac{5}{6}\)

Trước hết ta c/m BĐT: \(\left(a+b\right)^2\le2\left(a^2+b^2\right)\)

Thật vây, BĐT tương đương: \(a^2+2ab+b^2\le2a^2+2b^2\)

\(\Leftrightarrow a^2-2ab+b^2\ge0\Leftrightarrow\left(a-b\right)^2\ge0\) (luôn đúng)

Vậy \(\left(a+b\right)^2\le2\left(a^2+b^2\right)\Rightarrow a+b\le\sqrt{2\left(a^2+b^2\right)}\)

Áp dụng:

\(A\le\sqrt{2\left(9-x+x-1\right)}=\sqrt{2.8}=4\)

\(A_{max}=4\)

\(\frac{1}{x^2+3}+\frac{1}{x^2+9x+18}+\frac{1}{x^2+15x+54}=\frac{1}{2}\left(27-\frac{1}{x+9}\right)\)

\(\Leftrightarrow\frac{3}{x\left(x+3\right)}+\frac{3}{\left(x+3\right)\left(x+6\right)}+\frac{3}{\left(x+6\right)\left(x+9\right)}=27-\frac{1}{x+9}\)

Mà 

\(\frac{3}{x\left(x+3\right)}+\frac{3}{\left(x+3\right)\left(x+6\right)}+\frac{3}{\left(x+6\right)\left(x+9\right)}\)

\(=\frac{1}{x}-\frac{1}{x+3}+\frac{1}{x+3}-\frac{1}{x+6}+\frac{1}{x+6}-\frac{1}{x+9}\)

\(=\frac{1}{x}-\frac{1}{x+9}\)

\(\Rightarrow\frac{1}{x}=27\Rightarrow x=\frac{1}{27}\)

(627 - 138) : (x : 2) = 163

     489      : (x : 2) = 163

                    x : 2 = 489 : 163

                    x : 2 = 3

                    x      = 3 x 2

                    x      = 6

k mình nha

~Chúc các bạn học gioiỉ~

( 627  -  138 ) : ( X : 2 ) = 163

X : 2 = ( 627 - 138 ) : 163

X : 2 = 489 : 163

X : 2 = 3

X       = 3 x 2

X       = 6

( 627 - 138 ) : ( x : 2 ) = 163

489 : ( x : 2 ) = 163

x : 2 = 489 : 163

x : 2 = 3

x = 3 . 2

x = 6

vậy x = 6

hôm qua mik giải rùi mà bn

hôm wa mình ghi sai bài nên h mình ghi lại bài đó!

8, 725 x 3, 267 + 3, 267 x 1, 275 - 12, 627 = ( 8,725 + 1,275 ) x 3,267 - 12,627

                                                              = 10 x 3,267 - 12,627

                                                              = 32,67 - 12,627

                                                              = 20,43

8.725 x 3.267 + 3.267 x 1.725 - 12.627

= 3.267 x ( 8.725 + 1.725 ) - 12.627

= 3.267 x 10.45 - 12.627 

= 34.14015 - 12.627

= 21.51315 

8,725 x 3,267 + 3,267 x 1,725 - 12,627 = (8,725 + 1,725) x 3,267 - 12,627

                                                         =  10,45 x 3,267 - 12,627

                                                         =   34,14015 - 12,627

                                                         =   21,51315

   8,725 x 3,267 + 3,267 x 1,725 - 12,627

=  8,725 x 3,267 + 3,267 x 1,725 - 9,36 - 3,267

= 3,267 x ( 8,725 + 1,725 - 1 ) - 9,36

= 3,267 x 9,45 - 9,36

= 30;87315 - 9,36

= 21,51315