Question

resolva as equacoes de segundo grau:

Answer 1

Respostas:

1) {3,2}    2)   {2,6}     3) {-4,2}     4) ∅     5) {2}     6) {-3,4}      7) {1/3,-1/2}  8) {2, 1/3}

EQUAÇÕES DE 2º GRAU COMPLETAS:

1) x² - 5x + 6 = 0

  Δ = (-5)² - 4. 1. 6

  Δ = 25 - 24

  Δ = 1

  $x = \frac{- (-5) \pm\sqrt{1} }{2.1}$

  $x' = \frac{5+1}{2} \therefore x' = \frac{6}{2} \therefore x' = 3$

  $x'' = \frac{5-1}{2} \therefore x'' = \frac{4}{2} \therefore x''=2$

2) y² - 8y + 12 = 0

   $\triangle = (-8)^2-4.1.12$

   $\triangle = 64-48$

   $\triangle = 16$

   $x = \frac{-(-8) \pm\sqrt{16} }{2.1}$

   $x' = \frac{8+4}{2} \therefore x' = \frac{12}{2} \therefore x' = 6$

   $x''= \frac{8-4}{2} \therefore x'' = \frac{4}{2} \therefore x'' = 2$

3) x² + 2x - 8 = 0

   $\triangle = 2^2 - 4.1.(-8)$

   $\triangle = 4+32$

   $\triangle = 36$

   $x' = \frac{-2+\sqrt{36} }{2}\therefore x' = \frac{-2+6}{2}\therefore x'= \frac{4}{2} \therefore x' = 2$

   $x'' = \frac{-2-6}{2} \therefore x'' = \frac{-8}{2} \therefore = -4$

4) x² - 5x + 8 = 0

   $\triangle = (-5)^2 - 4.1.8$

   $\triangle = 25 - 32$

   $\triangle = - 7$

   $S = \phi$

5) 2y² - 8y + 8 = 0

   $\triangle = (-8)^2 - 4.2.8$

   $\triangle = 64 - 64$

   $\triangle = 0$

   $x = \frac{-(-8) \pm\sqrt{0} }{2.2} \therefore x = \frac{8\pm0}{4} \therefore x= \frac{8}{4} \therefore x= 2$

6) -x² + x + 12 = 0

   $\triangle = 1^2 - 4.(-1).12$

   $\triangle = 1 + 48$

   $\triangle = 49$

    $x'= \frac{-1+\sqrt{49} }{2(-1)} \therefore x' = \frac{-1+7}{-2} \therefore x' = \frac{6}{-2} \therefore x' = -3$

    $x'' = \frac{-1-7}{-2} \therefore x'' = \frac{-8}{-2} \therefore x'' = 4$

7) 6y² + y - 1 = 0

    $\triangle = 1^2 - 4.6.1$

    $\triangle = 25$

    $x' = \frac{-1+\sqrt{25} }{2.6} \therefore x' = \frac{-1+5}{12} \therefore x' = \frac{4}{12} \therefore x' = \frac{1}{3}$

    $x'' = \frac{-1-5}{12} \therefore x'' = \frac{-6}{12} \therefore x'' = \frac{-1}{2}$

8) 3x² - 7x + 2 = 0

    $\triangle = (-7)^2 - 4.3.2$

    $\triangle = 49-24$

    $\triangle = 25$

     $x' = \frac{(-7) + \sqrt{25} }{2.3} \therefore x' = \frac{7+5}{6} \therefore x' = \frac{12}{6} \therefore x' = 2$

     $x'' = \frac{7-5}{6} \therefore x'' = \frac{2}{6} \therefore x'' = \frac{1}{3}$

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