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If Q is the Mean Proportional Between P and R, Show That: Pqr (P + Q + R)3 = (Pq + Qr + Rp)3 - Mathematics

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

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APPEARS IN

Selina Concise Maths Class 10 ICSE
Chapter 7 Ratio and Proportion (Including Properties and Uses)
Exercise 7 (B) | Q 10 | Page 94
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