Question

Calcule as raízes das equações.

a) (x/5-5) . (x/5+5) = 0
b) 3 (x-2)² = 12
c) 2x² -3/4 = X + 1/4

Answer 1

a) (x/5-5) . (x/5+5) = 0

x/5 - 5 = 0 --> x - 25 = 0 ---> x = 25

x/5 + 5 = 0 --> x + 25 = 0 --> x = -25

b) 3 (x-2)² = 12

(x-2)² = 12/3 --> (x-2)² = 4

x² - 4x + 4 - 4 = 0

x² - 4x = 0

x(x - 4) = 0

x = 0 e (x-4) = 0 --> x = 4

As raízes são --> 0 e 4

c) 2x² -3/4 = x + 1/4

2x² - x = 1/4 + 3/4

2x² - x = 4/4 = 1

2x² - x - 1 = 0 ¨¨¨¨¨¨¨¨Báskara

Δ = b²-4ac = 1 + 8 = 9

√Δ = +-√9 = +-3

x = (1+3)/4 = 4/4 = 1

x" = (1-3)/4 = -2/4 = -1/2

Raízes: 1 e -1/2