Question

Rozwiąż równania:

1) x^2 - 5x - 24 = 0

2) (3x - 12) (x + 2) (x-1) = 0

3) 2x + 1 = 5

x

Answer 1

1)    

x^2  -   5x   -  24   =   0

Δ = 5² - 4 * 1 * (-24) = 25 + 96 = 121

√Δ = 11

x1 = (5 - 11)/2 = -6/2 = -3

x2 = (5 + 11)/2 = 16/2 = 8

 

odp. x = -3  lub  x = 8

 

2)   

(3x - 12) (x + 2) (x-1)  =  0

3x - 12 = 0   lub    x + 2 = 0    lub   x - 1 = 0

3x = 12        lub      x = -2      lub     x = 1

x = 4

 

odp. x = 4   lub   x = -2   lub    x = 1

 

3)    2x + 1     = 5              D: x≠ 0

           x

 

(2x + 1) / x - 5 = 0

(2x + 1) / x - (5x) / x = 0

[ (2x + 1) - 5x ] / x = 0

(2x + 1 - 5x) / x = 0

(-3x + 1) / x = 0

-3x + 1 = 0

-3x = -1

x = 1/3 

 

odp. x = 1/3