Question

Rozwiąż nierowność

(6-x)(x-4)<(x-1)(x-4)

Answer 1

(6-x)(x-4)<(x-1)(x-4)

6x - 24 - x² + 4x < x² - 4x - x + 4

-x² + 10x - 24 - x² + 5x - 4 < 0

-2x² + 15x - 28 < 0   / *(-1)

2x² - 15x + 28 > 0

Δ = 225 - 224 = 1

√Δ = 1

x1 = (15 - 1)/4 = 14/4 = 3,5

x2 = (15 + 1)/4 = 16/4 = 4

 

+++++                            ++++++

---------o---------------o------------->

          3,5     -------   4

x ∈ (-oo, 3,5) u (4, +oo)