O diálogo entre a Susana e o Pedro

Seja x o número de euros que tem o Pedro.

\[\begin{array}{*{20}{l}}{\begin{array}{*{20}{c}}{\frac{{{x^2}}}{2} = 5x}& \wedge &{x > 2}\end{array}}& \Leftrightarrow &{\begin{array}{*{20}{c}}{{x^2} – 10x = 0}& \wedge &{x > 2}\end{array}}\\{}& \Leftrightarrow &{\begin{array}{*{20}{c}}{x\left( {x – 10} \right) = 0}& \wedge &{x > 2}\end{array}}\\{}& \Leftrightarrow &{\begin{array}{*{20}{c}}{\left( {\begin{array}{*{20}{c}}{x = 0}& \vee &{x – 10 = 0}\end{array}} \right)}& \wedge &{x > 2}\end{array}}\\{}& \Leftrightarrow &{\begin{array}{*{20}{c}}{\left( {\begin{array}{*{20}{c}}{x = 0}& \vee &{x = 10}\end{array}} \right)}& \wedge &{x > 2}\end{array}}\\{}& \Leftrightarrow &{x = 10}\end{array}\]

Portanto, o Pedro tem 10 euros.