Question

resolva em r as inequações produto A) ( x - 1 ). ( x - 2 ) >= 0 B) (-2X + 1) . (3X - 6) > 0

Answer 1

A) ( x - 1 ). ( x - 2 ) > 0
x²-2x-x+2 > 0
x²-3x+2 > 0
Δ=b²-4.a.c
Δ=(-3)²-4.1.2
Δ=9-8
Δ=1

x¹=+3+1/2=2
x²=+3-1/2=1

B) (-2X + 1) . (3X - 6) > 0
-6x²+12x+3x-6 > 0
-6x²+9x-6 > 0
Δ=b²-4.a.c
Δ=9²-4.(-6).(-6)
Δ=64

x¹=-9+8/2=-1/2
x²=-9-8/2=-8,5

Espero ter ajudado!

Answer 2

A) (x-1).(x-2)>0
     x²-2x-x+2>0
     x²-3x+2>0

Δ=b²-4.a.c
Δ=(-3)²-4.1.2
Δ=9-8
Δ=1

x=-b+-√Δ/2a
x=3+-√1/2

x'=3+1/2 = 4/2 = 2
x"=3-1/2 = 2/2 = 1

B)(-2x+1).(3x-6)>0
    -6x²+12x+3x-6
    -6x²+15x-6

Δ=b²-4.a.c
Δ=15²-4.(-6).(-6)
Δ=225-144
Δ=81

x= -b+-√Δ/2a
x= -15+-√81/-12

x'= -15+9/-12 = -6/-12 = -1/-6
x"= -15-9/-12 = -24/-12 = -2