Question

Resolva em R as equações abaixo:

A) $\frac{x+2}{x} = 2$

B) $\frac{x-2}{4} + \frac{2x-8}{5} = 5$

C) (3x + 1) . (x - 1) - 3 (x + 2)² = -9

D) x² - 5x - 6 = 0

Answer 1

a)
x + 2     =  2
---------
   x

x + 2 = 2x
2 = 2x - x
2 = x
x = 2

***************************
b)
x - 2    +  2x - 8    =   5
--------     ----------
   4              5

5.(x - 2) + 4.(2x - 8) =  20.5
--------------------------    ------- 
     20                            20

5x - 10 + 8x - 32 = 100
13x - 42 = 100
13x = 100 + 42
13x = 142
x = 142/13
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
c)
(3x + 1). (x - 1) - 3 (x + 2)² = - 9
3x² - 3x + x - 1 - 3.(x² + 2.2x + 4) = - 9
3x² - 2x - 1 - 3.(x² + 4x + 4) = - 9
3x² - 2x - 1 - 3x² - 12x - 12 = - 9
- 2x - 12x - 1 - 12 = - 9
- 14x - 13 = - 9
- 13 + 9 = 14x
- 4 = 14x
14x = - 4
x =  - 4  (:2)
      -------
        14  (:2)

x =  - 2
       -------
          7

************************
d)

x² - 5x - 6 = 0
a = 1; b = - 5; c = - 6

Δ = b² - 4ac
Δ = (-5)² - 4.1.(-6)
Δ = 25 + 24
Δ = 49

x = - b +/- √Δ      =  - (-5) +/- √49
      ---------------       -------------------
             2a                      2.1

x =  5 + 7
      ---------  = 12/2 = 6
         2

x = 5 - 7
      -------- = - 2/2 = - 1
         2

R.: x = 6 e x = - 1