Question

Resolva as equações incompletas do 2° grau do tipo ax² + c = 0:

a) x² - 25 = 0

b) x² - 169 = 0

c) x² + 64 = 0

Answer 1

Letra A

$\sf {x}^{2} - 25 = 0$

$\sf {x}^{2} = 25$

$\sf x = \pm \: \sqrt{25}$

$\sf x = \pm \: 5$

$\red{\sf x_{1} = - 5}$

$\red{\sf x_{2} = 5}$

Letra B

$\sf {x}^{2} - 169 = 0$

$\sf {x}^{2} = 169$

$\sf x = \pm \: \sqrt{169}$

$\sf x = \pm \: 13$

$\red{\sf x_{1} = - 13}$

$\red{\sf x_{2} = 13}$

Letra C

$\sf {x}^{2} +64 = 0$

$\sf {x}^{2} = - 64$

$\sf x = \pm \: \sqrt{ - 64}$

$\sf x = \pm \: \sqrt{ - 1\cdot 64}$

$\sf x = \pm \: \sqrt{ - 1} \cdot \sqrt{64}$

$\sf x = \pm \: i \cdot 8$

$\sf x = \pm \: 8i$

$\red{\sf x_{1} = - 8i}$

$\red{\sf x_{2} = 8i}$