Question

Determine as raízes reais destas equações do 2º grau

Answer 1

a)
$( x + 1)^{2} = 16 \\ \\ x^{2} + 1^{2} - 16 = 0 \\ \\ x^{2} = 16 - 1 \\ \\ \boxed{x = \sqrt{15}}$

b)
 $5 x^{2} + 10x = 0 \\ \\ 5x + 10 = 0 \\ \\ x = - \frac{10}{5} \\ \\ \boxed{x = -2}$

c) 
$(x - 1)^{2} = 0 \\ \\ x^{2} - 1^{2} = 0 \\ \\ x = \sqrt{1} \\ \\ \boxed{x = 1}$

d)
 $(y + 5)^{2} = 81 \\ \\ y^{2} + 5^{2} - 81 = 0 \\ \\ y^{2} = - 25 + 81 \\ \\ \boxed{y = \sqrt{56}}$

e) 
$(x + 2)^{2} = 100 \\ \\ x^{2} +2^{2} = 100 \\ \\ x^{2} = 100 - 4 \\ \\ \boxed{x = \sqrt{96}}$

f) 
$(a - 3)^{2} = 36 \\ \\ a^{2} - 3^{2} = 36 \\ \\ a^{2} = 36 - 9 \\ \\ \boxed{a = \sqrt{27}}$

g) 
$10y^{2} - 200y = 0 \\ \\ 10y - 200 = 0 \\ \\ 10y = 200 \\ \\ y = \frac{200}{10} \\ \\ \boxed{y = 20}$

h) 
$30b^{2} + 270b = 0 \\ \\ 30b + 270 = 0 \\ \\ 30b = -270 \\ \\ b = \frac{270}{30} \\ \\ \boxed{b = 9}$