Question

resolva as seguintes inequações quociente:
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Answer 1

Resposta:

a) x+2 / x-1 > 0

x+2 > 0.(x-1)

x > -2

b) 3x-1 / -x +2 < 0

3x-1 < 0.(-x+2)

3x < 1

x < 1/3

c) 2x+1 / x-2 > 0

2x+1 / x-2 > 0.(x-2)

2x+1 > 0

2x > -1

x > -1/2

d) (x-1).(x+3) / x-5 > 0

(x-1).(x+3) / x-5 > 0.(x-5)

(x-1).(x+3) > 0

x²+3x-x-3 > 0

x²+2x-3 > 0

a=1

b=2

c=-3

Δ= b²-4.a.c

Δ= 2² -4.1.-3

Δ= 4 +12

Δ=16

X= -b±√Δ / 2a

X= -2±√16 / 2.1

X= -2±4 / 2

X'= -2+4 / 2 = 2 / 2 = 1

e) (2x-1).(-x+3) / x+2 ≤ 0

(2x-1).(-x+3) / x+2 ≤ 0.(x+2)

(2x-1).(-x+3) ≤ 0

-2x²+6x+x-3 ≤ 0

-2x²+5x-3 ≤ 0

a= -2

b= 5

c= -3

Δ= b²-4.a.c

Δ= (5)²-4.-2.-3

Δ= 25-24

Δ= 1

X= -5±√1 / 2.-2

X= -5±1 / -4

X'= -5+1 / -4 = -4 / -4 = 1

X''= -5-1 / -4 = -6 / -4 = 3/2

{X ∈ R | 1 < X < 3/2}