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Anettt [7]
2 years ago
7

Let A = {x : 2x² + 3x - 2 = 0} and B = {x : x² + 3x - 4 = 0 } find (A U B) × (A Π B)​

Mathematics
1 answer:
ivann1987 [24]2 years ago
8 0

Given :

  • A = {x: 2x² + 3x - 2 = 0 }
  • B = {x : x² + 3x - 4 = 0 }

To find :

  • (A U B ) × (A Π B )

Solution :-

<u>The </u><u>first </u><u>set </u><u>is </u><u>,</u>

  • A ={x : 2x² + 3x - 2 = 0}

<u>Solving</u><u> </u><u>the </u><u>Quadratic</u><u> equation</u><u> </u><u>,</u>

  • 2x² + 3x - 2 = 0
  • 2x² + 4x - x - 2 = 0
  • 2x( x + 2) -1( x + 2 ) = 0
  • (2x -1) ( x + 2) = 0
  • x = 0.5 , -2

<u>Hence</u><u> </u><u>,</u>

  • A ={0.5, -2}

<u>The </u><u>second</u><u> </u><u>set </u><u>is </u><u>,</u>

  • B ={ x :x² + 3x - 4 = 0 }

<u>Solving</u><u> the</u><u> Quadratic</u><u> equation</u><u> </u><u>,</u>

  • x² + 3x - 4 = 0
  • x² + 4x - x - 4 = 0
  • x( x + 4)-1 ( x +4) = 0
  • (x + 4) ( x -1) = 0
  • x = 1 , -4

<u>Hence</u><u> </u><u>,</u>

  • B ={1,4}

<u>Now </u><u>,</u>

  • A U B = { 0.5 , 1 , 4 , -2}
  • A Π B = {∅ }

Since AΠ B is a null set , hence ,

  • A × B = {∅}
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