Colaborativo De álgebra Act 6

3) Resuelva las siguientes inecuaciones y halle el conjunto solución.

x^3-〖8x〗^2+19x-12>0

R= (1)^3 〖-8(1)〗^2+19(1)-12

R= 1-8+19-12

R= 0 (x-1)

R= (3)^3 〖-8(3)〗^2+19(3)-12

R= 27-72+57-12

R=0. (x-3)

(x-1) (x-3) (x-4) > 0

1 U 2 U 3 U 4

X > 4 U 1< x < 3 U ⌀U ⌀

X>4 U 1< X< 3

(X+4 )/(5-X)≤ (2-X )/(X-3)

((X+4)(X-3)-(2-X)(5-X) )/((5-X)(X-3)) ≤0

(x^2-3X+4X-12-(10-2X-5X+x^2))/((5-X)(X-3)) ≤0

(6X-22 )/((5-X)(X-3)) ≤0

6X-22 ≥ 0 ^ (5-X)(-3) ≤ 0

a). 6X-22 ≥ 0 ^ 5-X≥ 0 ^ x-3 ≤ 0

6X ≥ 22

X ≥ 11/3

b). 6X-22 ≥ 0 ^ 5-X≤ 0 ^ x-3 ≥ 0

6X ≥ 22 ^ x ≥5 ^ x ≥ 3

X ≥ 11/3

2). a). 6X-22 ≤ 0 ^ (5-X)(-3) ≥ 0

6X-22 ≤ 0 ^ 5-X≥ 0 ^ x-3≥ 0

6X ≤ 22 ^ 5-X≥ 0 ^ x-3≥ 0

X ≤ 11/3 ^ x ≤5^ x≥3

b). 6X-22 ≤ 0 ^ 5-X≥0 ^ x-3 ≤ 0

6X ≤ 22

X ≤ 11/3 ^ x≥ 5^ x≤3

a ⋃ b = ⌀ ⋃ x ≥ 5

= x ≥ 5

a ⋃ b = x ≤ 3 ⋃ ⌀

= x ≤ 3

1 ⋃ 2 = x ≥ 5 ⋃ x ≤ 3

3 ≥ x ≥ 5

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