Question

If A = {x / 6x² + x – 15 = 0}, B = {x / 2x² – 5x – 3  = 0}, C = {x / 2x – x – 3 = 0}, then find

(i) (A ∪ B ∪ C)

(ii) (A ∩ B ∩ C)

Answer 1

A = [x/6x² + x – 15 = 0)

6x² + x – 15 = 0

6x² + 10x – 9x – 15 = 0

2x(3x + 5) – 3(3x + 5) = 0

(3x + 5) (2x – 3) = 0

3x + 5 = 0 or 2x – 3 = 0

x = -5/3 or x =  3/2

A = {-5/3, 3/2 }

B = {x/2x² – 5x – 3 = 0}

2x² – 5x – 3 = 0

2x² – 6x + x – 3 = 0

2x(x – 3) + 1(x – 3) = 0 

(x – 3)(2x + 1) = 0

x – 3 = 0 or 2x + 1 = 0

x = 3 or x = -1/2

B = ( -1/2, 3)

C = {x/2x² – x – 3 = 0}

2x² – x – 3 = 0

2x² – 3x + 2x – 3 = 0

x(2x – 3) + 1(2x – 3) = 0

(2x – 3) (x + 1) = 0

2x – 3 = 0 or x + 1 = 0

x = 3/2 or x = -1

C = {-1, 3/2}

(i) A ∪ B ∪ C =

{-5/3, 3/2}U{-1/2, 3} U {-1, 3/2} =

{-5/3, 1, -1/2, 3/2, 3}

(ii) A ∩ B ∩ C = { }