Question

Solutia ecuatiei x/2-2x+1/3=5/6 este
Descompune în factori expresia 25x²-(2x+1)²este

Answer 1

     
$\frac{x}{2}- \frac{2x+1}{3} = \frac{5}{6} \;\;\;\;\;\;\;\;\;\;(Aducem \;la \;acelasi \;numitor) \\ \\ \frac{3x}{6}- \frac{2(2x+1)}{6} = \frac{5}{6} \;\;\;\;\; |*6\\ \\ 3x-2(2x+1)=5 \\ 3x-4x-2-5=0 \\ -x-7=0\;\;\;\;\;|*(-1) \\ x+7=0 \\ x=\boxed{-7}$


$\text{------------------------------------} \\ \\ 25x^2 - (2x+1)^2= \\ =(5x)^2-(2x+1)^2= \\ =[5x-(2x+1)][5x+(2x+1)]= \\ =[5x-2x-1)][5x+2x+1]= \boxed{(3x-1)(7x+1)}$