1. ## 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?

2. ## 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?

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

Originally Posted by AaPa
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 $\displaystyle x^2= a$. 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.)

thanks.