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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 - ICSE Class 10 - Mathematics

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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.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 Solution for Selina ICSE Concise Mathematics for Class 10 (2018-2019) (2017 to Current)
Chapter 7: Ratio and Proportion (Including Properties and Uses)
Ex.7B | Q: 10

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Solution If Q is the Mean Proportional Between P and R, Show That: Pqr (P + Q + R)3 = (Pq + Qr + Rp)3 Concept: Proportions.
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