Question

Tìm x biết

a)\(||3x-\frac{7}{3}|-2|=7\)

b) Cho \(\frac{a}{2b}=\frac{b}{2c}=\frac{c}{2d}=\frac{d}{2a}\)(a, b, c, d > 0). Tính

A = \(\frac{2013a-2012b}{c+d}+\frac{2013b-2012c}{a+d}+\frac{2013c-2012d}{a+b}+\frac{2013d-2012a}{b+c}\)

Answer 1

                                                       Bài giải

a, \(\left| |3x-\frac{7}{3} | -2\right|=7\)

\(\Rightarrow\orbr{\begin{cases}|3x-\frac{7}{3}|-2=-7\\|3x-\frac{7}{3}|-2=7\end{cases}}\)                 \(\Rightarrow\orbr{\begin{cases}|3x-\frac{7}{3}|=-5\text{ ( loại) }\\|3x-\frac{7}{3}|=9\end{cases}}\)         \(\Rightarrow\text{ }\left|3x-\frac{7}{3}\right|=9\)        \(\Rightarrow\orbr{\begin{cases}3x-\frac{7}{3}=-9\\3x-\frac{7}{3}=9\end{cases}}\)                             \(\Rightarrow\orbr{\begin{cases}3x=\frac{-20}{3}\\3x=\frac{34}{3}\end{cases}}\)                             \(\Rightarrow\orbr{\begin{cases}x=-\frac{20}{9}\\x=\frac{34}{9}\end{cases}}\)

                 \(\Rightarrow\text{ }x\in\left\{-\frac{20}{9}\text{ ; }\frac{34}{9}\right\}\)