Introducción a resolver ecuaciones con raíces cuadradas

$\begin{array}{rl}\sqrt{2x-5}& =7\\ \\ {\left(\sqrt{2x-5}\right)}^2& =7^2\\ \\ 2x-5& =49\\ \\ 2x& =54\\ \\ x& =27\end{array}$‍

$\begin{array}{rl}\sqrt{2x-5}& =7\\ \\ \sqrt{2(27)-5}& \stackrel{?}{=}7\\ \\ \sqrt{54-5}& \stackrel{?}{=}7\\ \\ \sqrt{49}& \stackrel{?}{=}7\\ \\ 7& =7\end{array}$‍

$\begin{array}{rl}\sqrt{10-3x}& =\sqrt{2x+5}\\ \\ {\left(\sqrt{10-3x}\right)}^2& ={\left(\sqrt{2x+5}\right)}^2\\ \\ 10-3x& =2x+5\\ \\ 10-5& =2x+3x\\ \\ 5& =5x\\ \\ 1& =x\end{array}$‍

$\begin{array}{rl}\sqrt{10-3x}& =\sqrt{2x+5}\\ \\ \sqrt{10-3\left(1\right)}& \stackrel{?}{=}\sqrt{2\left(1\right)+5}\\ \\ \sqrt{7}& =\sqrt{7}\\ \end{array}$‍

$\begin{array}{rl}\sqrt{5x-4}& =x-2\\ \\ {\left(\sqrt{5x-4}\right)}^2& =(x-2{)}^2\\ \\ 5x-4& =x^2-4x+4\\ \\ 0& =x^2-9x+8\\ \\ 0& =(x-8)(x-1)\end{array}$‍

$\begin{array}{rl}\sqrt{5x-4}& =x-2\\ \\ \sqrt{5(8)-4}& \stackrel{?}{=}8-2\\ \\ \sqrt{36}& \stackrel{?}{=}6\\ \\ 6& =6\end{array}$‍

$\begin{array}{rl}\sqrt{5x-4}& =x-2\\ \\ \sqrt{5(1)-4}& \stackrel{?}{=}1-2\\ \\ \sqrt{1}& \stackrel{?}{=}-1\\ \\ 1& \ne -1\end{array}$‍