Question

Se x(1-x) = $\frac{1}{4}$ , então:

a) x= $\frac{1}{4}$
b) x= $\frac{1}{2}$
c) x= 1
d) x= $\frac{1}{8}$
e) x= 0

Answer 1

x ( 1 - x) = 1
                4

4x (1 - x) = 1
4x - 4x² = 1
- 4x² + 4x - 1 = 0
a = - 4, b = 4; c = - 1

Δ = b² - 4ac
Δ = 16 - 4.(-4).(-1)
Δ = 16 - 16
Δ = 0

x = - b +/-√Δ
          2a

x = - 4 +/- √0
         2(-4)

x = - 4
      - 8

x = 4  (:4) =   1
      8  (:4)      2

x = 1/2  = (b)