Question

podaj zbior rownan i nierownosci:

a) 4t^2-12t=-9

b)-1/2x^2+x>=0

c) (c-1)^2<3x-5

Answer 1

a) 4t²-12t=-9

4t²-12t+9=0

Δ=(-12)²-4*4*9=144-144=0

t=12/8=1,5

 

b)-½x²+x ≥ 0

x(-½x+1) ≥ 0

x=0 ∨ x=2

x∈<0;2>

 

c) (x-1)²<3x-5 

x²-2x+1 < 3x -5 

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