Advertisements
Advertisements
Question
If p, q and r in continued proportion, then prove the following:
(p2 - q2)(q2 + r2) = (q2 - r2)(p2 + q2)
Advertisements
Solution
p : q :: q : r => q2 = pr1
LHS (p2 _ q2)( q2 + r2)
= (p2 -(pr)2)(pr)2 + r2)
= p3r - p2r2 + p2r2 - pr3
= pr (p2 - r2)
RHS
(q2 - r2)(p2 + q2)
= ((pr)2-r2 )(p2+ (pr)2)
= p3r - p2r2 + p2t2 - pr3
= pr(p2 - r2)
LHS = RHS. Hence, proved.
APPEARS IN
RELATED QUESTIONS
Find the third proportional to a2 – b2 and a + b.
Find the third proportion to the following :
3 and 15
If a, b, c are in continued proportion and a(b – c) = 2b, prove that: `a - c = (2(a + b))/a`.
Find the third proportional to `5(1)/(4) and 7.`
Find the mean proportion of: 5 and 80
Determine if the following numbers are in proportion:
22, 33, 42, 63
Find the value of x in each of the following proportions:
51 : 85 : : 57 : x
Write (T) for true and (F) for false in case of the following:
32 kg : Rs 36 : : 8 kg : Rs 9
Find the value of x if 5 : 3 : : x : 6.
What number must be added to each of the numbers 4, 6, 8, 11 in order to get the four numbers in proportion?
