Advertisements
Advertisements
Question
If a, b, c, d are in continued proportion, prove that: a : d = triplicate ratio of (a – b) : (b – c)
Advertisements
Solution
a, b, c, d are in continued proportion
∴ `a/b = b/c = c/d` = k(say)
∴ c = dk, b = ck = dk. k = dk2,
a = bk = dk2. k = dk3
a : d = triplicate ratio of (a – b) : (b – C)
= (a – b)3 : (b – c)3
L.H.S. = a : d
= `a/d`
= `(dk^3)/d`
= k3
R.H.S. = `(a - b)^3/(b - c)^3`
= `(dk^3 - dk^2)^3/(dk^2 - dk)^3`
= `(d^3k^6(k - 1)^3)/(d^3k^3(k - 1)^3`
= k3
∴ L.H.S. = R.H.S.
APPEARS IN
RELATED QUESTIONS
Check whether the following numbers are in continued proportion.
1, 2, 3
If x, 12 and 16 are in continued proportion! find x.
Find two nurnbers whose mean proportional is 12 and the third proportional is 324.
Find the two numbers such that their mean proprtional is 24 and the third proportinal is 1,536.
Determine if the following numbers are in proportion:
33, 121, 9, 96
If a, b, c and d are in proportion, prove that: `(a + c)^3/(b + d)^3 = (a(a - c)^2)/(b(b - d)^2)`
If a, b, c, d are in continued proportion, prove that: (a + d)(b + c) – (a + c)(b + d) = (b – c)2
If the weight of 40 books is 8 kg, then the weight of 15 books is 3 kg
If a, b, c and d are in proportion, the value of `(8a^2 - 5b^2)/(8c^2 - 5d^2)` is equal to ______.
What is the term "d" called in the expression a : b :: c : d?
