Usa-se a fórmula de Bháskara para se resolver equações do 2° grau, e sua fórmula é:
[tex]\boxed{X = \frac{-b+ou- \sqrt{\Delta=b^2-4(a)(c)} }{2\cdot\ a} }[/tex]
[tex]5x^2-x-4=0[/tex]
[tex]\Delta = (-1)^2-4(5)(-4)\\\\ \Delta = 1+80\\\\ \boxed{\Delta=81}[/tex]
[tex]X = \frac{-(-1)+ou- \sqrt{81} }{2\cdot5} \\\\ X = \frac{1+ou-9}{10} \\\\ x^i = \frac{1+9}{10} = \frac{10}{10} =1\\\\ x^i^i = \frac{1-9}{10} = \frac{-8}{10} = \frac{-4}{5} [/tex]
Solução do exercício :
[tex]\boxed{S(1, \frac{-4}{5}) }[/tex]
[tex]-7x^2+x+5=0(-1)\\\\ 7x^2-x-5=0\\\\ \Delta = (-1)^2-4(7)(-5)\\\\ \Delta = 1+35\\\\ \boxed{\Delta=36}[/tex]
[tex]X = \frac{-(-1)+ ou- \sqrt{36} }{2\cdot7}\\\\ X = \frac{1+ou-6}{14} \\\\ x^i = \frac{1+6}{14} = \frac{7}{14} = \frac{1}{2} \\\\ x^i^i = \frac{1-6}{7} = \frac{-5}{7} [/tex]
Solução :
[tex]\boxed{\boxed{S( \frac{1}{2} , \frac{-5}{7} )}}[/tex]
[tex]8x^2=(x-1)^2\\\\ 8x^2 = x^2-2x+1\\\\ 7x^2+2x-1=0\\\\ \Delta = (2)^2-4(7)(-1)\\\\ \Delta = 4+28\\\\ \boxed{\Delta=32}[/tex]
[tex]X = \frac{-(+2)+ou- \sqrt{32} }{2\cdot7} \\\\ X = \frac{-2+ou-4 \sqrt{2} }{14} \\\\ x^i = \frac{-2+4 \sqrt{2} }{14} = \frac{-1+2 \sqrt{2} }7} \\\\ x^i^i = \frac{-2-4 \sqrt{2} }{14} = \frac{-1-2 \sqrt{2} }{7} [/tex]
Solução:
[tex]\boxed{S(\frac{-1+2 \sqrt{2} }7 ,\frac{-1-2 \sqrt{2} }7)} [/tex]
