Question

Como resolver a Equação 2x² -2x -1=0 ?

Answer 1

2x-2x -1=0 ~~>2x-2x=0+1~~>2x-2x=0~~>0+1=1~~>1divido por 0=0

Answer 2

$2x^2 -2x -1 =0$

A = 2
B = -2
C = -1

bhaskara
$\boxed{\boxed{ \frac{-b\pm \sqrt{b^2-4ac} }{2a} }}\\\\= \frac{-(-2)\pm \sqrt{(-2)^2-4*2*(-1)} }{2*2}= \frac{2\pm \sqrt{4+8} }{4}= \frac{2\pm \sqrt{12} }{4}$

fatorando a raiz de 12
mmc
12|2
6 | 2
3 | 3
12 = 2²*3
$\sqrt{12}= \sqrt{2^2*3}= \sqrt{2^2}* \sqrt{3}\\\\ \sqrt{12}=2 \sqrt{3}$

calculando as raízes
$\frac{2\pm2 \sqrt{3} }{4}= \frac{2*(1\pm \sqrt{3}) }{4}= \frac{(1\pm \sqrt{3})}{2} \\\\ x' = \frac{1- \sqrt{3} }{2}\\\\ x''=\frac{1+ \sqrt{3} }{2}$