Question

If q is the mean proportional between p and r, show that: pqr (p + q + r)³ = (pq + qr + rp)³

Answer 1

Given, q is the mean proportional between p and r.
⇒ q² = pr

L.HS = `pqr(p + q + r)^3`

`= qq^2 (p + q + r)^3`        [∵ q^2 = pr]

`= [q(p +  q + r)]^3`

`= (pq + q^2 + qr)^3`

`= (pq + pr + qr)^3`      ` [∵ q^2 = pr]`

= R.H.S