\(\frac{1}{2}\cdot\frac{18}{14}+\frac{1}{2}\cdot\frac{3}{14}-\frac{1}{2}\cdot\frac{7}{14}\)

\(=\frac{1}{2}\left(\frac{18}{14}+\frac{3}{14}-\frac{7}{14}\right)\)

\(=\frac{1}{2}\cdot1=\frac{1}{2}\)

a:Sửa đề: \(\sqrt{x+\sqrt{14x-49}}+\sqrt{x-\sqrt{14x-49}}=\sqrt{14}\)

ĐKXĐ: x>=7/2

\(\sqrt{x+\sqrt{14x-49}}+\sqrt{x-\sqrt{14x-49}}=\sqrt{14}\)

=>\(\sqrt{14x+14\cdot\sqrt{14x-49}}+\sqrt{14x-14\sqrt{14x-49}}=14\)

=>\(\sqrt{14x-49+2\cdot\sqrt{14x-49}\cdot7+49}+\sqrt{14x-49-2\cdot\sqrt{14x-49}\cdot7+49}=14\)

=>\(\sqrt{\left(\sqrt{14x-49}-7\right)^2}+\sqrt{\left(\sqrt{14x-49}+7\right)^2}=14\)

=>\(\left|\sqrt{14x-49}-7\right|+\left|\sqrt{14x-49}+7\right|=14\)

=>\(\left|\sqrt{14x-49}-7\right|=14-\sqrt{14x-49}-7=7-\sqrt{14x-49}\)

=>\(\sqrt{14x-49}-7\le0\)

=>\(\sqrt{14x-49}\le7\)

=>14x-49<=49

=>14x<=98

=>x<=7

=>7/2<=x<=7

b: ĐKXĐ:x>=1

Sửa đề: \(\sqrt{x+2\sqrt{x-1}}-\sqrt{x-2\sqrt{x-1}}=1\)

=>\(\sqrt{x-1+2\cdot\sqrt{x-1}\cdot1+1}-\sqrt{x-1-2\cdot\sqrt{x-1}\cdot1+1}=1\)

=>\(\sqrt{\left(\sqrt{x-1}+1\right)^2}-\sqrt{\left(\sqrt{x-1}-1\right)^2}=1\)

=>\(\sqrt{x-1}+1-\left|\sqrt{x-1}-1\right|=1\)

=>\(\left|\sqrt{x-1}-1\right|=\sqrt{x-1}\)

=>\(\left[\begin{array}{l}\sqrt{x-1}-1=\sqrt{x-1}\\ \sqrt{x-1}-1=-\sqrt{x-1}\end{array}\right.\Rightarrow\left[\begin{array}{l}-1=0\left(loại\right)\\ 2\sqrt{x-1}=1\end{array}\right.\)

=>\(\sqrt{x-1}=\frac12\)

=>x-1=1/4

=>x=5/4(nhận)

X+\(\dfrac{2}{7}\)=\(\dfrac{1}{2}\)

X     = \(\dfrac{1}{2}\)-\(\dfrac{2}{7}\)
X     = \(\dfrac{3}{14}\)
Chọn đáp án A. \(\dfrac{3}{14}\)

A

\(x+\left(x+1\right)+\left(x+2\right)+....+13+14=14\Leftrightarrow x+\left(x+1\right)+....+13\Leftrightarrow x=-13\)

\(25+24+23+....+x+\left(x-1\right)+\left(x-2\right)=25\Leftrightarrow24+....+\left(x-2\right)=0\Leftrightarrow x-2=-24\)

\(\Leftrightarrow x=-22\)

bạn làm rõ hơn đi

Ta có : \(\frac{1}{2}+\frac{1}{14}+\frac{1}{35}+...+\frac{1}{x\left(x+3\right):2}=\frac{9}{14}\)

\(\Rightarrow2\left(\frac{1}{4}+\frac{1}{28}+\frac{1}{70}+...+\frac{1}{x\left(x+3\right)}\right)=\frac{9}{14}\)

\(\Rightarrow2.\frac{1}{3}\left(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{x\left(x+3\right)}\right)=\frac{9}{14}\)

\(\Rightarrow\frac{2}{3}\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{x}-\frac{1}{x+3}\right)=\frac{9}{14}\)

\(\Rightarrow1-\frac{1}{x+3}=\frac{27}{28}\)

\(\Rightarrow\frac{1}{x+3}=\frac{1}{28}\)

=> x + 3 = 28

=> x  = 25 

mình cần gấp

\(x+\left(x+1\right)+\left(x+2\right)+....+14=14\Rightarrow x+\left(x+1\right)+...+13=0\Rightarrow\left(x+13\right)\left(14-x\right)=0\)

\(x=14\text{ hoặc -13}\)

A = 7/7.17 + 7/17.27 + 7/27.37 + ............ +7/1997.2007

A=7/10 ( 10/7.17 + 10/17.27 + 10/27.37 + ................+10/1997.2007)

A= 7/10  ( 1/7 -1/17 + 1/17 - 1/27 + 1/27 - 1/37 +...............+ 1/1997 - 1/2007)

A= 7/10 (1/7 - 1/2007)

A= 7/10 . 2000/14049

A=200/2007

bây h mk có vc rùi tích đúng nha tối mk lm típ cho

1, -15 + \(x\) = -14 - (-57)

   -15 + \(x\)  = -14 + 57

             \(x\) = -14 + 57  + 15

             \(x\) = 43 + 15

             \(x\) = 58

2, (-14) + \(x\) - 7 = -10

    -14 + \(x\) - 7 = -10

     - 21 + \(x\)    = - 10

                \(x\)   = -10 + 21

                 \(x\) = 11

Giải:

a) \(4\left(x+1\right)-\left(3x+1\right)=14\)

\(\Leftrightarrow4x+4-3x-1=14\)

\(\Leftrightarrow x+3=14\)

\(\Leftrightarrow x=14-3=11\)

Vậy ...

b) \(-2\left(x-1\right)-\left(2-3x\right)=2\left(x+1\right)-4\)

\(\Leftrightarrow-2x+2-2+3x=2x+2-4\)

\(\Leftrightarrow x=2x-2\)

\(\Leftrightarrow x-2x=-2\)

\(\Leftrightarrow-x=-2\)

\(\Leftrightarrow x=2\)

Vậy ...

c) \(-\left(x-3\right)+\left(4x-1\right)-14=2\left(x-2\right)-5\)

\(\Leftrightarrow-x+3+4x-1-14=2x-4-5\)

\(\Leftrightarrow3x-15=2x-9\)

\(\Leftrightarrow3x-2x=-9+15\)

\(\Leftrightarrow x=6\)

Vậy ...