#### Question

If q is the mean proportional between p and r prove that `(p^3 + q^3 + r^3)/(p^2q^2r^2) = 1/p^3 + 1/q^3 = 1/r^3`

#### Solution

Since q is the mean proportional between p and r

`q^2 = pr`

L.H.S = `(p^3 + q^3 + r^3)/(p^2q^2r^2)`

`= (p^3 + (pr)q + r^3)/(p^3r^3)`

`= 1/r^3 + q/(p^2r^2) + 1/p^3`

`= 1/r^3 + q/(q^2)^2 + 1/p^3`

`= 1/r^3 + 1/q^3 + 1/p^3`

= R.H.S

Is there an error in this question or solution?

Solution If Q is the Mean Proportional Between P and R Prove that (P^3 + Q^3 + R^3)/(P^2q^2r^2) = 1/P^3 + 1/Q^3 = 1/R^3 Concept: Proportions.