harmonic mean: Find harm. mean, given geo, arith means

[Math wiz ya rite 09]

Find the harmonic mean of two numbers whose geometric mean is 13 and the arithmetic mean is 15.

I know that the arithmetic mean gives me:

. . .(a + b)/2 = 15

...so a + b = 30. And the geometric mean gives me:

. . .sqrt(a*b) = 13

...so ab = 169. I know that the harmonic mean of a and b is:

. . .(2ab) / (a + b).

How do I find what the harmonic mean of the two numbers is, though?

 

[skeeter]

Re: harmonic mean

Find the harmonic mean of two numbers whose geometric mean is 13 adn the arithmetic mean is 15.

I know that

(a+b)/2 = 15 or that a+b=30

sqrt(a*b)= 13 or that ab = 169

I know that the harmonic mean is (2ab)/(a+b).

How do I find what the harmonic mean of two numbers is, though?

Looks like the solution is staring you in the face.

 

[stapel]

Um... maybe plug the values you have for a + b and ab into the formula "(2ab) / (a + b)"...? And then simplify...?

Eliz.

 

[Math wiz ya rite 09]

omg
how did i miss that!

LOL


thanks