Question

Resolva a equação |x² - 6x| = 9

Answer 1

$|x^2 - 6x| = 9$

Existe duas possibilidades:

x² - 6x = 9 ou x² - 6x = -9

$x^{2} - 6x = 9 \\ x^2 - 6x - 9 = 0 \\ \\ a=1,\,b=-6,\,c=-9 \\ \\ \Delta=b^2-4*a*c \\ \Delta = (-6)^2-4*1*(-9) \\ \Delta=36+36 \\ \Delta=72 \\ \\ x= \frac{-b \pm \sqrt {\Delta}}{2*a} \\ \\ x= \frac{-(-6)\pm\sqrt{72}}{2*1} \\ \\ x = \frac{6\pm6\sqrt{2}}{2} \\ \\ x'= \frac{6+6\sqrt{2}}{2} = 3 + 3\sqrt{2} \\ \\ x'' = \frac{6 - 6\sqrt{2}}{2} = 3 - 3\sqrt{2}$

$x^2 - 6x = -9 \\ x^2 -6x + 9=0 \\ \\ a=1,\,b=-6,\,c=9 \\ \\ \Delta=(-6)^2-4*1*9 \\ \Delta=36-36 \\ \Delta=0 \\ \\ x= \frac{-(-6)\pm\sqrt{0}}{2*1} \\ \\ x=\frac{6\pm0}{2} \\ \\ x'=x''= \frac{6}{2} = 3$

$V = \{ 3\pm3\sqrt{2} \, ,\,3 \}$