Resposta :
[tex]x^{2} = 72[/tex]
[tex]x^{2} - 72 = 0[/tex]
[tex]\Delta = b^2-4ac[/tex]
[tex]\Delta = 0^2-4(1)(-72)[/tex]
[tex]\Delta = 0+288[/tex]
[tex]\Delta = 288[/tex]
//
[tex]x = \frac{-b\pm \sqrt{\Delta}}{2a}[/tex]
[tex]x = \frac{-0\pm \sqrt{288}}{2*1}[/tex]
[tex]x = \frac{-0\pm \sqrt{288}}{2}[/tex]
Fatorando o 288
288 | 2
144 | 2
72 | 2
36 | 2
18 | 2
09 | 3
3 | 3
1
Portanto:
[tex]\sqrt{288} = \sqrt{2^{2}*2^{2}*3^{2}*2}[/tex]
Os que estão elevados ao quadrado, vão sair da raiz.
[tex]\sqrt{288} = \sqrt{2^{2}*2^{2}*3^{2}*2} = 12\sqrt{2}[/tex]
[tex]x = \frac{-0\pm 12\sqrt{2}}{2}[/tex]
_____________________
[tex]x' = \frac{-0 +12\sqrt{2}}{2}[/tex]
[tex]x' = \frac{12\sqrt{2}}{2}[/tex]
[tex]\boxed{x' = 6\sqrt{2}}[/tex]
_____________________
[tex]x'' = \frac{-0 - 12\sqrt{2}}{2}[/tex]
[tex]x'' = \frac{-12\sqrt{2}}{2}[/tex]
[tex]\boxed{x'' = -6\sqrt{2}}[/tex]
[tex]\boxed{S =6\sqrt{2}, -6\sqrt{2}}}[/tex]