Question

hơi khó, giúp vs

tìm x biết

\(|2x-3|=\left(\dfrac{1}{2}\right)^y\) và \(y=\dfrac{\dfrac{3}{7}-\dfrac{3}{11}+\dfrac{3}{101}}{\dfrac{5}{7}-\dfrac{5}{11}+\dfrac{5}{101}}+\dfrac{\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{4}}{\dfrac{5}{4}-\dfrac{5}{6}+\dfrac{5}{8}}\)

Answer 1

\(y=\dfrac{3\left(\dfrac{1}{7}-\dfrac{1}{11}+\dfrac{1}{101}\right)}{5\left(\dfrac{1}{7}-\dfrac{1}{11}+\dfrac{1}{101}\right)}+\dfrac{\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{4}}{\dfrac{5}{2}.\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{4}\right)}=\dfrac{3}{5}+\dfrac{2}{5}=1\)

\(|2x-3|=\left(\dfrac{1}{2}\right)^1=\dfrac{1}{2}\Rightarrow\left[{}\begin{matrix}2x-3=\dfrac{1}{2}\Rightarrow x=\dfrac{7}{4}\\2x-3=-\dfrac{1}{2}\Rightarrow x=\dfrac{5}{4}\end{matrix}\right.\)

Answer 2

bt làm mỗi ý 2

Answer 3

`y = (3/7 - 3/11 + 3/101)/(5/7 - 5/11 + 5/101) + (1/2 - 1/3 + 1/4)/(5/4 - 5/6 + 5/8)`

`y = (3 . (1/7 - 1/11 + 1/101))/(5 . (1/7 - 1/11 + 1/101)) + (1/2 - 1/3 + 1/4)/(5/2.(1/4 - 1/6 + 1/8))`

`y = 3/5 + 2/5`

`y = 5/5 = 1`

ta thấy :

`|2x - 3| = (1/2)^1`

`=> 2x - 3 = 1/2`

`=> 2x      = 1/2 + 3`

`=> 2x      = 7/2`

`=>  x      = 7/2 : 2`

`=> x      = 7/4`