Question

Rozwiąż równanie:

a) (3x-1)/2x = 2/(3x-1)

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

c) (x-3)/(2-x) = 1/2

Answer 1

a) (3x-1)/2x = 2/(3x-1) ---- x ≠ 0 i x≠ 1/3

(3x - 1) * (3x - 1) = 2 * 2x

9x² - 6x + 1 = 4x

9x² - 10x + 1 = 0

Δ = 100 - 36 = 64

√Δ = 8

x1 = (10 - 8) / 18 = 1/9

x2 = (10 + 8) / 18 = 1

 

 

b) (x-1)/(x+5) = 0 ---- x ≠ - 5

x - 1 = 0

x = 1

 

c) (x-3)/(2-x) = 1/2

2(x - 3) = 2 - x   ----  x ≠ 2

2x - 6 = 2 - x

2x + x = 2 + 6

3x = 8

x = 8/3