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Question
If q is the mean proportional between p and r, show that: pqr(p + q + r)3 = (pq + qr + rp)3.
Solution
Given, q is the mean proportional between p and r.
⇒ q2 = pr
L.H.S = pqr(p + q + r)3
= qq2(p + q + r)3
= q3(p + q + r)3 ...[∵ q2 = pr]
= [q(p + q + r)]3
= (pq + q2 + qr)3
= (pq + pr + qr)3 ...[∵ q2 = pr]
= R.H.S
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