Question

\(\left(2x-1\right)^2-\dfrac{1}{4}=2\)
\(\left(-2\dfrac{1}{5}+\dfrac{2}{7}-\dfrac{12}{13}\right)-\left(-\dfrac{5}{7}+\dfrac{1}{13}\right)\)

Answer 1

( 2x -1)² - \(\dfrac{1}{4}\) = 2                            ( -2\(\dfrac{1}{5}\)  + \(\dfrac{2}{7}\) - \(\dfrac{12}{13}\)) - ( - \(\dfrac{5}{7}\)+\(\dfrac{1}{13}\))

(2x -1)²        = 2 + \(\dfrac{1}{4}\)                   =     -\(\dfrac{11}{5}\) + \(\dfrac{2}{7}\) - \(\dfrac{12}{13}\) + \(\dfrac{5}{7}\) - \(\dfrac{1}{13}\)

(2x -1) ²        = \(\dfrac{9}{4}\)                         = - \(\dfrac{11}{5}\) + ( \(\dfrac{2}{7}+\dfrac{5}{7}\)) - ( \(\dfrac{12}{13}+\dfrac{1}{13}\))

\(\left[{}\begin{matrix}2x-1=\dfrac{3}{2}\\2x-1=-\dfrac{3}{2}\end{matrix}\right.\)                          = - \(\dfrac{11}{5}\) + 1 - 1

\(\left[{}\begin{matrix}2x=\dfrac{3}{2}+1\\2x=-\dfrac{3}{2}+1\end{matrix}\right.\)                          = -11/5 

\(\left[{}\begin{matrix}2x=2,5\\2x=-0,5\end{matrix}\right.\)

\(\left[{}\begin{matrix}x=1,25\\x=-0,25\end{matrix}\right.\)