Question

Resolva as equações do 2° grau:

a)x+2/2 + 2/x-2 = -1/2
b)5/x² + 1/x - 6 =0
c)3/x - 4 = x + 6/2x
d)x-5/x-1 +x +1 =0

Answer 1

Boa noite Srayzaa

a)

(x + 2)/2 + 2/(x - 2) + 1/2 = 0 

(x + 2) + 4/(x - 2) + 1  = 0 

(x + 2)*(x - 2)/(x - 2) + 4/(x - 2) + (x - 2)/(x - 2) = 0

x² - 4 + 4 + x - 2 = 0

x² + x - 2 = 0

delta
d² = 1 + 8 = 9
d = 3

x1 = (-1 + 3)/2 = 2/2 = 1
x2 = (-1 - 3)/2 = -4/2 = -2

b) 

y = 1/x

5y² + y - 6 = 0

delta
d² = 1 + 120 = 121
d = 11

y1 = (-1 + 11)/10 = 10/10 = 1,  x1 = 1/y1 = 1
y2 = (-1 - 11)/10 = -12/10 = -6/5,  x2 = 1/y2 = -5/6 

c)

3/x - 4 = x + 6/2x

3/x - 4 = x + 3/x

x = -4 

d)

(x - 5)/(x - 1) + (x + 1) = 0

(x - 5)/(x - 1) + (x + 1)*(x - 1)/(x - 1) = 0

x - 5 + x² - 1 = 0
x² + x - 6 = 0

delta
d² = 1 + 24 = 25
d = 5

x1 = (-1 + 5)/2 = 4/2 = 2
x2 = (-1 - 5)/2 = -6/2 = -3