# Math Help - find the mean

1. ## find the mean

If the geometric mean of a and b is 10 and the harmonic mean of a and b is 8, find the value of the following without determining the values of a and b.

1/a + 1/b

2. Hello, Mr_Green!

Are you sure of the wording of the problem?
. . It seems to be much too simple.

If the geometric mean of a and b is 10 . ← not needed
and the harmonic mean of a and b is 8,
find the value of (1/a + 1/b) without determining the values of a and b.

. . . . . . . . . . . . . 2
We are given: . -------- . = . 8
. . . . . . . . . . . .1 . . 1
. . . . . . . . . . . .-- + --
. . . . . . . . . . . .a . . b

. . . . . .1 . . 1 . . . . 1
Then: . -- + -- . = . --
. . . . . .a . . b . . . . 4

3. i meant:

1/(a^2) + 1/(b^2)

4. Hello again, Mr_Green!

If the geometric mean of a and b is 10 and the harmonic mean of a and b is 8,
find the value of: .1/a² + 1/b²
We are given: .√(ab) = 10 . . ab = 100 . . 2/ab = 1/50 .[1]

I have already shown that: .1/a + 1/b .= .1/4

Square both sides: .1/a² + 2/ab + 1/b² .= .1/16
. . . . . . . . . . . . . . . . . . . .
Substitute [1]: . . . 1/a² + 1/50 +1/b² .= .1/16

Therefore: .1/a² + 1/b² .= .1/16 - 1/50 .= .17/400