Question

Resolva a equação |x² - 6x| = 9. Escolha uma:
a. S = {3±32√, 3}
b. S = {3±20√, 3}
c. NDA
d. S = {3±28√, 2}
e. S = {3±30√, 3

Answer 1

$\mathbf{Se\ |x^2-6x|=9,\ temos\ apenas\ duas\ possibilidades:}$

$\mathrm{\mathbf{1)}\ \boxed{\mathrm{x^2-6x=9}}\ \to\ x^2-6x-9=0\ \to\ a=1\ \|\ b=-6\ \|\ c=-9}\\\\ \mathrm{x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-(-6)\pm\sqrt{(-6)^2-4.1.(-9)}}{2.1}=}\\\\ \mathrm{=\dfrac{6\pm\sqrt{36+36}}{2}=\dfrac{6\pm\sqrt{2.(36)}}{2}=\dfrac{6\pm6\sqrt{2}}{2}=\boxed{\mathrm{3\pm3\sqrt{2}}}}$

$\mathbf{2)}\ \boxed{\mathrm{x^2-6x=-9}}\ \to\ \mathrm{x^2-6x+9=0\ \to\ a=1\ \|\ b=-6\ \|\ c=9}\\\\ \mathrm{x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-(-6)\pm\sqrt{(-6)^2-4.1.9}}{2.1}=}\\\\ \mathrm{\dfrac{6\pm\sqrt{36-36}}{2}=\dfrac{6\pm0}{2}=\boxed{\mathrm{3}}}$

$\boxed{\boxed{\mathbb{S}=\{3\pm3\sqrt{2};\ 3\}}}$