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