\(\dfrac{1}{1.4}+\dfrac{1}{4.7}+\dfrac{1}{7.10}+...+\dfrac{1}{x\left(x+3\right)}=\dfrac{125}{376}\)

\(\Leftrightarrow\dfrac{1}{3}\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+...+\dfrac{1}{x}-\dfrac{1}{x+3}\right)=\dfrac{125}{376}\)

\(\Leftrightarrow\dfrac{1}{3}\left(1-\dfrac{1}{x+3}\right)=\dfrac{125}{376}\left(x\ne0;x\ne-3\right)\)

\(\Leftrightarrow\dfrac{x+3-1}{x+3}=\dfrac{3.125}{376}\Leftrightarrow\dfrac{x+2}{x+3}=\dfrac{3.125.}{376}.\dfrac{\left(x+3\right)}{x+3}\)

\(\Leftrightarrow376\left(x+2\right)=3.125.\left(x+3\right)\)

\(\Leftrightarrow376x+752=375x+1125\)

\(\Leftrightarrow376x-375x=1125-752\Leftrightarrow x=373\left(x\in N^{\cdot}\right)\)

a, ( 3 - 0,6) - ( 7 + 3\(\dfrac{1}{4}\) - \(\dfrac{8}{5}\)) - ( 9 - 2\(\dfrac{1}{4}\))

 = 2,4 - (7 + 3,25 - 1,6) - (9 - 2,25)

= 2,4 - 7 - 3,25 + 1,6 - 9 + 2,25

= (2,4 + 1,6) - (7+ 9) - ( 3,25 - 2,25)

= 4 - 16 - 1

= - 12 - 1

= -13

b, ( - \(\dfrac{5}{8}\) + \(\dfrac{7}{6}\) - \(\dfrac{0}{8}\)) - (\(\dfrac{5}{6}\) - \(\dfrac{7}{8}\) - 1,4) + ( \(\dfrac{3}{4}\) + \(\dfrac{5}{3}\) + \(\dfrac{12}{5}\))

 = - \(\dfrac{5}{8}\) + \(\dfrac{7}{6}\) - \(\dfrac{5}{6}\) + \(\dfrac{7}{8}\) + \(\dfrac{7}{5}\) + \(\dfrac{3}{4}\) +  \(\dfrac{5}{3}\) + \(\dfrac{12}{5}\)

= (- \(\dfrac{5}{8}\) + \(\dfrac{7}{8}\)) + (\(\dfrac{7}{6}\) - \(\dfrac{5}{6}\)) + ( \(\dfrac{7}{5}\) + \(\dfrac{12}{5}\)) + \(\dfrac{3}{4}\) + \(\dfrac{5}{3}\)

= \(\dfrac{1}{4}\) + \(\dfrac{1}{3}\) + \(\dfrac{19}{5}\) + \(\dfrac{3}{4}\) + \(\dfrac{5}{3}\)

= (\(\dfrac{1}{4}\) + \(\dfrac{3}{4}\)) + ( \(\dfrac{1}{3}\) + \(\dfrac{5}{3}\)) + \(\dfrac{19}{5}\)

= 1 + 2 + 3,8

= 6,8

`3x-15/(5*8)-15/(8*11)-15/(11*14)-...-15/(47*50)=2 1/10`

`3x-(15/(5*8)+15/(8*11)+15/(11*14)+...+15/(47*50))=21/10`

`3x-5(3/(5*8)+3/(8*11)+3/(11*14)+...+3/(47*50))=21/10`

`3x-5(1/5-1/8+1/8-1/11+1/11-1/14+...+1/47-1/50)=21/10`

`3x-5(1/5-1/50)=21/10`

`3x-5*9/50=21/10`

`3x-9/10=21/10`

`3x=21/10+9/10`

`3x=3`

`x=1`

s+e+x

\(\left(14+8\right).2.5+14.8-18=314\left(m^2\right)\)

Diện tích xq  là:

  2 . ( 14 + 8 ) . 5 = 220(m²)

DT trần nhà là;

  14 . 8 = 112 (m²)

DT cần sơn là:

  ( 220 + 112 ) - 18 =  314 ( m² )

Vậy ..

\(\sqrt{5-3x}=9\) (ĐK: \(x\le\dfrac{5}{3}\))

\(\Leftrightarrow5-3x=9^2\)

\(\Leftrightarrow-3x=81-5\)

\(\Leftrightarrow-3x=76\)

\(\Leftrightarrow x=\dfrac{76}{-3}\left(tm\right)\)

\(\sqrt[]{5-3x}=9\left(x\le\dfrac{5}{3}\right)\)

\(\Rightarrow5-3x=81\Rightarrow3x=-76\Rightarrow x=-\dfrac{76}{3}\)

\(\sqrt{3x-7}=4\)

\(\sqrt{\left(3x-7\right)^2}=4^2\) (ĐK: \(x\ge \)\(\dfrac{7}{3}\))

\(3x-7=16\)

\(3x=16+7=23\)

\(x=\dfrac{23}{3}\)

\(\sqrt{3x-7}=4\) (ĐK: \(x\ge\dfrac{7}{3}\))

\(\Leftrightarrow3x-7=4^2\)

\(\Leftrightarrow3x-7=16\)

\(\Leftrightarrow3x=16+7\)

\(\Leftrightarrow3x=23\)

\(\Leftrightarrow x=\dfrac{23}{3}\)

\(\sqrt[]{2x-3}=7\left(x\ge\dfrac{3}{2}\right)\)

\(\Rightarrow2x-3=49\Rightarrow2x=52\Rightarrow x=26\)

\(\sqrt[]{2-3x}=4\left(x\le\dfrac{2}{3}\right)\)

\(\Rightarrow2-3x=16\Rightarrow3x=-14\Rightarrow x=-\dfrac{14}{3}\)

\(\sqrt{2-3x}=4\)

\(\sqrt{\left(2-3x\right)^2}=4^2\) (ĐK: \(x\le\) \(\dfrac{2}{3}\))

\(2-3x=16\)

\(3x=2-16\)

\(3x=-14\)

\(x=-\dfrac{14}{3}\)

Ta có góc của màng hình tivi là góc vuông nên đường cheo của tivi là:

\(\sqrt{72^2+120^2}=24\sqrt{34}\left(cm\right)\)

Đổi: \(24\sqrt{34}\left(cm\right)\approx55\left(inch\right)\)

Vậy: ...