Advertisements
Advertisements
प्रश्न
If a, b, c, d are in continued proportion, prove that: a : d = triplicate ratio of (a – b) : (b – c)
Advertisements
उत्तर
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
संबंधित प्रश्न
Find two numbers such that the mean proportional between them is 12 and the third proportional to them is 96.
Find the third proportional to a2 – b2 and a + b.
What number must be added to each of the number 16, 26 and 40 so that the resulting numbers may be in continued proportion?
Find two numbers whose mean proportional is 18 and the third proportional is 486.
What number must be added to each of the numbers 16, 26 and 40 so that the resulting numbers may be in continued proportion?
Find two numbers such that the mean proportional between them is 28 and the third proportional to them is 224.
If `a/c = c/d = c/f` prove that : `bd f[(a + b)/b + (c + d)/d + (c + f)/f]^3` = 27(a + b)(c + d)(e + f)
If a, b, c are in continued proportion, prove that: a2 b2 c2 (a-4 + b-4 + c-4) = b-2(a4 + b4 + c4)
If 7 : 5 is in proportion to x : 25, then ‘x’ is
Determine if the following are in proportion.
33, 121, 9, 96
