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Math Help - GP : -2/7,x,-7/2

  1. #1
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    GP : -2/7,x,-7/2

    X has two values -1 and 1. But if we use geometric mean=sqrt(ab)=x, we get only x=1. Why does this formula give only one solution?
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  2. #2
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    Re: GP : -2/7,x,-7/2

    Hey AaPa.

    What is a and b? Can you please explain what you are trying to do, what assumptions you have, and what data/constants you have?
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  3. #3
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    Re: GP : -2/7,x,-7/2

    Quote Originally Posted by AaPa View Post
    X has two values -1 and 1. But if we use geometric mean=sqrt(ab)=x, we get only x=1. Why does this formula give only one solution?
    I think you mean that if a and b are two numbers whose product is 1 then there geometric mean is X= sqrt(ab)= sqrt(1)= 1.

    You are mistaken about the square root function. For any positive number, a, there exist two numbers, x, such that x^2= a. However, the square root is defined as the positive one. That is \sqrt{1}= 1, \sqrt{4}= 2, \sqrt{9}= 3, etc.. -1, -2, -3 are NOT square roots.

    (The reason we write the \pm in "if x^2= a then x= \pm\sqrt{a}" is because the \sqrt{a} does NOT include both.)
    Last edited by HallsofIvy; November 17th 2013 at 04:34 PM.
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  4. #4
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    Re: GP : -2/7,x,-7/2

    thanks.
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