Question

Rozwiąż nierówność
2x²-2x-24<0

6x≥5x²

-6x²-5x=4=0

x²-5x>-6

Answer 1

A) 2x²-2x-24<0
Δ=b²-4ac=(-2)²-4*2*(-24)=4+96=100
√Δ=10
x₁=-b+√Δ/2a=2+10/4=12/4=3
x₂=-b-√Δ/2a=2-10/4=8/4=2

b)6x≥5x²
-5x²+6x≥0
x(-5x+6)≥0
x=0

-5x+6=0
-5x=-6
x=1⅕

c)-6x²-5x+4=0
Δ=(-5)²-4*(-6)*4=25+96=121
√Δ=11
x₁=5+11/-12=16/-12=1¾
x₂=5-11/-12=-6/-12=½


d)x²-5x>-6
x²-5x+6>0
Δ=(-5)²-4*1*6=25-24=1
√Δ=1
x₁=5+1/2=6/2=3
x₂=5-1/2=4/2=2

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Answer 2

1.
2x^-2x-24< 0 (^-kwadrat)
delta =(-2)^- 4*2*(-24) = 196
Vd =V196 =14
X1 =(2-14)/4 = -3
X2 =(2 +14)/4 = 4
Odp. X<4
2.
6x>=5x^
6x-5x^>= 0
x(6-5x)>= 0
X1 = 0,lub
6-5x>= 0
-5x>= -6/(-5)
x<= 6/5
x<=1 1/5
Odp. 1 1/5=>X>=0
3.
-6x^-5 =4= 0 ?
4.
x^-5x> -6
x^-5x +6>0
delta = 25-24=1
X1 =(5-1)/2 =2
X2 =(5+1)/2 =3
Odp.X>2