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Lv 5
? asked in Science & MathematicsMathematics · 10 years ago

please solve |x^2 - 4| > 0?

1 Answer

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  • 10 years ago
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    Think about, when is this *not* true? We know that the absolute value of anything is *at least* 0. The only time when |x^2 - 4| > 0 could not be true is if:

    |x^2 - 4| = 0

    x^2 - 4 = 0 ... (since the only x such that |x| = 0 is x = 0)

    x^2 = 4

    x = -2 or 2

    If x = -2 or 2, then |x^2 - 4| = 0. Otherwise, |x^2 - 4| > 0, so the answer is all real numbers except -2 or 2. In interval notation:

    (-infinity, -2) U (-2, 2) U (2, infinity)

    Hope that helps!

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