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Define the set X = : x2 − 9 = 0, x is an integer\.

Mathematics

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Answer

X={−3,3}X = \{-3, 3\}

Step-by-step solution

3 steps

The image shows a set defined as X={x:x2−9=0,x is an integer}X = \{x : x^2 - 9 = 0, x \text{ is an integer}\}. To find XX, we need to solve the equation x2−9=0x^2 - 9 = 0 and then select the solutions that are integers.

  1. Solve the equation x2−9=0x^2 - 9 = 0.

    x2−9=0x^2 - 9 = 0

    Add 9 to both sides:

    x2=9x^2 = 9

    Take the square root of both sides:

    x=±9x = \pm\sqrt{9} x=±3x = \pm 3

    So, the solutions are x=3x = 3 and x=−3x = -3.

  2. Identify the integer solutions.

    Both 3 and −3-3 are integers.

  3. Write the set XX.

    The set XX consists of all integers xx that satisfy x2−9=0x^2 - 9 = 0.

    X={−3,3}X = \{-3, 3\}

    The value of XX is:

    X={−3,3}\boxed{X = \{-3, 3\}}
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