Question

resolva as equações :
x²+7+12=0
3x²-6x=0
6x²-9=0

Answer 1

$x^2+7x+12=0\\\\ \Delta=7^2-4\cdot1\cdot12\\ \Delta=49-48\\ \Delta=1\\\\ x= \dfrac{-7\pm \sqrt{1} }{2\cdot1}= \dfrac{-7\pm1}{2}\begin{cases}x_1= \dfrac{-7+1}{2}=-3\\\\ x_2= \dfrac{-7-1}{2}=-4 \end{cases}$


$3x^2-6x=0\\\\ x(3x-6)=0\\\\ x_1=0~~~~e~~~~3x-6=0\\ ~~~~~~~~~~~~~~~~~~~3x=6\\ ~~~~~~~~~~~~~~~~~~~~x=6/3\\ ~~~~~~~~~~~~~~~~~~~~x_2=2$


$6x^2-9=0\\ 6x^2=9~~(divide~por~3)\\ 2x^2=3\\\\ x^2= \dfrac{3}{2}\\\\ x=\pm \sqrt{ \dfrac{3}{2} }\\\\ x=\pm \dfrac{ \sqrt{3} }{ \sqrt{2} }=\pm \dfrac{ \sqrt{3}\cdot \sqrt{2} }{ \sqrt{2}\cdot \sqrt{2} }=\pm \dfrac{ \sqrt{6} }{2}\\\\\\ x_1= \dfrac{ \sqrt{6} }{2}~~e~~x_2=- \dfrac{ \sqrt{6} }{2}$