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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- Nov 17th 2013, 05:11 AM #1

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- Nov 17th 2013, 03:15 PM #2

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- Nov 17th 2013, 03:55 PM #3

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## Re: GP : -2/7,x,-7/2

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 $\displaystyle x^2= a$. However, the square root is defined as the**positive**one. That is $\displaystyle \sqrt{1}= 1$, $\displaystyle \sqrt{4}= 2$, $\displaystyle \sqrt{9}= 3$, etc.. -1, -2, -3 are NOT square roots.

(The reason we write the $\displaystyle \pm$ in "if $\displaystyle x^2= a$ then $\displaystyle x= \pm\sqrt{a}$" is**because**the $\displaystyle \sqrt{a}$ does NOT include both.)

- Nov 18th 2013, 07:37 AM #4

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