Question

Questão 10. Resolva as seguintes equações.


a) x2 - 9x = 0

b)x2 - 100 = 0

c) x2 - 6x + 5 = 0​

Answer 1

Resposta:

a) x' = 9  | x" = 0

b) x = ± 10

c) x' = 5  | x" = 1

Explicação passo a passo:

a) x² - 9x = 0

a = 1  | b = -9  | c = 0

$\frac{9 +/- \sqrt{(-9)^{2} - 4 . 1 . 0 } }{2.1}\\\\\frac{9 +/- \sqrt{81 - 4 . 0} }{2}\\\\\frac{9+/-\sqrt{81 - 0} }{2}\\\\\frac{9 +/- \sqrt{81} }{2}\\\\\frac{9 +/- 9}{9}\\\\x' = \frac{9 + 9}{2} = \frac{18}{2} = 9\\\\x" = \frac{9-9}{2} = \frac{0}{2} = 0$

b) x² - 100 = 0

x² = 100

x = ± √100

x = ± 10

c) x² - 6x + 5 = 0

a = 1  | b = -6  | c = 5

$\frac{6+/- \sqrt{(-6)^{2} - 4 . 1 . 5 } }{2.1}\\\\\frac{6+/-\sqrt{36 - 4 . 5} }{2}\\\\\frac{6+/- \sqrt{36-20} }{2}\\\\\frac{6+/-\sqrt{16} }{2} \\\\\frac{6+/-4}{2} \\\\x' = \frac{6 +4}{2} = \frac{10}{2} = 5\\\\x" = \frac{6-4}{2} = \frac{2}{2} = 1$

BONS ESTUDOS!!!