Question

Rozwiąż nierówność

a) 2x-3/4 - 3x-2/3 = x/2

b) x-2/2 - 2 (x+2)² < 5,5 - (2x-1) (2x+1)/2

To ważne proszę o pomoc

Answer 1

 

 

Answer 2

a) (2x-3)/4 – (3x-2)/3 = x/2    /* 12

3(2x-3) – 4(3x-2) = 6x

6x -9 -12x + 8 = 6x

6x -6x -12x = - 8 +9

-12x = 1   /(-12)

x= -1/12

 

b)( x-2)/2 - 2 (x+2)² < 5,5 -[(2x-1) (2x+1)]/2      /* 2

x-2 -4(x+2)² < 11 - (2x-1) (2x+1)

x-2 –(x² +4x +4) < 11 -(4x² -1)

x-2 –x² -4x -4 + 4x² -11 - 1  < 0

3x² -3x -18 < 0

Δ = b² -4ac = (-3)² - 4 *3 (-18) = 9 +216 =225

√Δ = √225 = 15

x₁ = (-b-√Δ)/2a = (3 – 15)/6 = -12/6 = -2

 x₂ = (-b+√Δ)/2a = (3 + 15)/6 = 18/6 = 3