Question

Rozwiąż nierówności:
[(12x-4)-4(2x+1)]*-2x(8x-1)>2

Answer 1

[(12x-4)-4(2x+1)]*-2x(8x-1)>2
(12x-4-8x-4) * (-16x² +2x) > 2
(4x-8) * (-16x² + 2x)>2
-64x³+8x²+128x²-16x > 2 |:2
-32x³+ 70x²- 8x - 1 >0

Answer 2

[(12x-4)-4(2x+1)]*-2x(8x-1)>2
[12x-4-8x-4]*(-16x²+2x)>2
(4x-8)*(-16x²+2x)>2
(2x-4)*(-8x²+x)>1
x(2x-4)*(-8x+1)>1
x(-16x²+2x+32x-4)>1
x(-16x²+34x-4)-1>0
x>1
-16x²+34x-4>0
-8x²+17x-2>0
Δ=17²-4*-8*-2=225
√Δ=15
x₁=(-17-15)/-16=2
x₂=(-17+15)/-16=-¹/₈

x∈(-¹/₈;2) ∧ x>1
x∈(1;2)

Może tak? :d

Answer 3

[(12x-4)-4(2x+1)]*-2x(8x-1)>2
[12x-4-8x-4]*-16x²+2x>2
[4x-8]*-16x²+2x>2
16x²-64x+64-16x²+2x>2
-64x+2x>2-64
-62x>-62 /(-62)
x>1
Myślę że "tak to leciało";)