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?

Results 1 to 4 of 4

- Nov 17th 2013, 06:11 AM #1

- Joined
- Mar 2012
- From
- India
- Posts
- 85

- Nov 17th 2013, 04:15 PM #2

- Joined
- Sep 2012
- From
- Australia
- Posts
- 6,416
- Thanks
- 1676

- Nov 17th 2013, 04:55 PM #3

- Joined
- Apr 2005
- Posts
- 18,677
- Thanks
- 2640

## 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 . However, the square root is defined as the**positive**one. That is , , , etc.. -1, -2, -3 are NOT square roots.

(The reason we write the in "if then " is**because**the does NOT include both.)

- Nov 18th 2013, 08:37 AM #4

- Joined
- Mar 2012
- From
- India
- Posts
- 85