Question

As raízes da equação 0,25x^2 - x + 0,25=0 são

Answer 1

$0,25x^{2}-x+0,25=0\\(1/4)*x^{2}-x+(1/4)=0$

Multiplicando todos os membros por 4:

$4*(1/4)*x^{2}-4*x+4*(1/4)=4*0\\1*x^{2}-4x+1=0\\x^{2}-4x+1=0$

$\Delta=b^{2}-4*a*c\\\Delta=(-4)^{2}-4*1*1\\\Delta=16-4\\\Delta=12\\\Delta=3*4\\\sqrt{\Delta}=\sqrt{3}*\sqrt{4}\\\sqrt{\Delta}=\sqrt{3}*2\\\sqrt{\Delta}=2\sqrt{3}$

$x=(-b\pm\sqrt{\Delta})/2a\\x=(-[-4]\pm2\sqrt{3})/(2*1)\\x=(4\pm2\sqrt{3})/2$

Colocando 2 em evidência:

$x=2*(2\pm\sqrt{3})/2\\x=2\pm\sqrt{3}\\\\x'=2+\sqrt{3}\\x''=2-\sqrt{3}$

$S=\{2-\sqrt{3},~2+\sqrt{3}\}$