Question

RESOLVA AS SEGUINTES EQUAÇÕES:
a) ($(x+3)^2 = 2x (x+7)$
b) $2x^2 -2\sqrt{2}$ x = -1
(A letra b é 2x^2 -2 raiz de dois x = -1)

Answer 1

a)

(X + 3)^2 = 2x.(x + 7)
x^2 + 2.x.3 + 9 = 2x^2 + 14x
x^2 + 6x + 9 = 2x^2 + 14x
0 = 2x^2 - x^2 + 14x - 6x - 9
0 = x^2 + 8x - 9
x^2 + 8x - 9 = 0
a = 1; b = 8; c = - 9
∆ = b^2-4ac
∆ = 8^2 - 4.1.(-9)
∆ = 64 + 36
∆ = 100

x = [ - b +/- √∆]/2a
x = [ - 8 +/- √100]/2.1
x = [ - 8 +/- 10]/2
x' = [ - 8 - 10]/2 = - 18/2 = - 9
x" = [ - 8 + 10]/2 = 2/2 = 1

B)
2x^2 - 2√2 x = - 1
2x^2 - 2x^2 x + 1 = 0
a = 2; b = - 2√2; c = 1
∆ = b^2-4ac
∆ = (-2√2)^2 - 4.2.1
∆ = 4.2 - 8
∆ = 8 - 8
∆ = 0

x = [- b +/- √∆]/2a
x = [ - ( -2√2)]/ 2.2
x = 2√2/4
x = √2/2