Advertisements
Advertisements
Question
If q is the mean proportional between p and r, show that: pqr(p + q + r)3 = (pq + qr + rp)3.
Advertisements
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
RELATED QUESTIONS
Find the third proportional to a – b and a2 – b2
Check whether the following numbers are in continued proportion.
2, 4, 8
Find two numbers whose mean proportional is 18 and the third proportional is 486.
Find the value of x in the following proportions : 2.5 : 1.5 = x : 3
Find the mean proportion of: 5 and 80
Find the value of x in each of the following proportions:
51 : 85 : : 57 : x
If a, b, c, d are in continued proportion, prove that: (a + d)(b + c) – (a + c)(b + d) = (b – c)2
A recipe calls for 1 cup of milk for every `2 1/2` cups of flour to make a cake that would feed 6 persons. How many cups of both flour and milk will be needed to make a similar cake for 8 people?
The mean proportion between `3 + 2sqrt(2)` and `3 - 2sqrt(2)` is ______.
The table, given below, shows the values of x and y, where x is proportional (directly proportional) to y.
| x | A | 24 | 15 |
| y | 12 | B | 20 |
The values of A and B are:
