Question

A soma de um número com seu quadrado é 72. quais os números?

Answer 1

$\mathtt{x^2 + x = 72} \\ \mathtt{x^2 +x -72 = 0} \\ \\ \mathtt{a = 1} \\ \mathtt{b = 1} \\ \mathtt{c = -72} \\ \\ \mathtt{\Delta = b^2 -4~.~a~.~c} \\ \\ \mathtt{\Delta = 1^2-4~.1~.~(-72)} \\ \mathtt{\Delta = 1 + 288} \\ \mathtt{\Delta = 289} \\ \\ \mathtt{\dfrac{-b +- \sqrt{\Delta}}{2~.~a}} \\ \\ \\ \mathtt{\dfrac{-1+-~ \sqrt{289}}{2~.~1}} \\ \\ \\ \mathtt{\dfrac{-1 +- ~17}{2}}$

$\mathtt{x' = \dfrac{-1 + 17}{2}} \\ \\ \mathtt{x' = \dfrac{16}{2}} \\ \\ \boxed{\mathtt{x' =8 }} \\ \\ \\ \mathtt{x'' = \dfrac{-1 - 17}{2}}$ 
$\mathtt{x'' = \dfrac{-18}{2}} \\ \\ \boxed{\mathtt{x'' = -9}} \\ \\ \\ \boxed{\boxed{\mathtt{Resposta : S: -9~~~~e~~~~8}}}$