Question

If A = {x/6x² + x - 15 = 0}

B = {x/2x² - 5x - 3 = 0}

C = {x/2x² - x - 3 = 0} then

find (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 = `{3,(-1)/2}`

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 = `{3/2, -1}`

A ∩ B ∩ C = `{(-5)/3,3/2} ∩ {3,(-1)/2} ∩ {3/2, -1}`

A ∩ B ∩ C = ϕ