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Math Help - Properties of Absolute Values

  1. #1
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    Properties of Absolute Values

    Explain why the given statement is true for any numbers c and d. HINT GIVEN: Look at the properties of absolute value. sqrt[9c^2 - 18cd + 9d^2] = 3|c - d|
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    Can you simplify the LHS a bit? Maybe do a little factoring?
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    Quote Originally Posted by fdrhs1984 View Post
    Explain why the given statement is true for any numbers c and d. HINT GIVEN: Look at the properties of absolute value. sqrt[9c^2 - 18cd + 9d^2] = 3|c - d|
    Inside the radicand, I divided every term by 9 and reduced the trinomial to be sqrt[c^2 - 2cd + d^2]. I then factored and got (c - d)(c - d) in the radicand.
    Where do I go from here?
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    Ok, so you can write the LHS as 3 sqrt[(c-d)^2]. Do you recognize this now?

    How is sqrt[x^2] related to |x|?
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