Question

[Nguyễn Bảo Ngọc]

Tìm x: (2x+1/2)*(3/4-x)=0

Tính nhanh: 2/10*12+2/12*14+2/14*16+...+2/48*50

Answer 1

[An Hoà]

( 2x + 1 / 2 ) * ( 3 / 4 - x ) = 0

=> 2x + 1 / 2 = 0 hoặc 3 / 4 - x = 0

               2x  = - 1 / 2             x = 3 / 4 

                 x  = - 1 / 4                

Vậy x = -1 / 4 hoặc x = 3 / 4

2 / 10 * 12 + 2 / 12 * 14 + 2 / 14 * 16 + ... + 2 / 48 * 50

= 1 / 10 - 1 / 12 + 1 / 12 - 1 / 14 + 1 / 14 + 1 / 16 + .... + 1 / 48 - 1/ 50

= 1 / 10 - 1 / 50 

= 2 / 25

Answer 2

[QuocDat]

Tìm x : \(\left(2x+\frac{1}{2}\right)\left(\frac{3}{4}-x\right)=0\)

\(\Rightarrow\orbr{\begin{cases}2x+\frac{1}{2}=0\\\frac{3}{4}-x=0\end{cases}\Rightarrow\orbr{\begin{cases}x=\frac{-1}{2}\\x=\frac{3}{4}\end{cases}}}\)

Tính nhanh : \(\frac{2}{10.12}+\frac{2}{12.14}+...+\frac{2}{48.50}\)

\(=2\left(\frac{1}{10.12}+\frac{1}{12.14}+...+\frac{1}{48.50}\right)\)

\(=2.\frac{1}{2}\left(\frac{1}{10}-\frac{1}{12}+\frac{1}{12}-\frac{1}{14}+...+\frac{1}{48}-\frac{1}{50}\right)\)

\(=\frac{1}{10}-\frac{1}{50}\)

\(=\frac{2}{25}\)