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
Given four quantities p, q, r and s are in proportion, show that
q2(p - r) : rs (q - s) =(p2- q2- pq): ( r2-s2-rs).
If p, q and r in continued proportion, then prove the following:
(p2 - q2)(q2 + r2) = (q2 - r2)(p2 + q2)
Find the third proportional to `5(1)/(4) and 7.`
Write (T) for true and (F) for false in case of the following:
30 bags : 18 bags : : Rs 450 : Rs 270
Write (T) for true and (F) for false in case of the following:
45 km : 60 km : : 12 h : 15 h
If `a/c = c/d = c/f` prove that : `(a^2)/(b^2) + (c^2)/(d^2) + (e^2)/(f^2) = "ac"/"bd" + "ce"/"df" + "ae"/"df"`
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 and d are in proportion, prove that: `abcd [(1/a^2 + 1/b^2 + 1/c^2 + 1/d^2]` = a2 + b2 + c2 + d2
Are the ratios 25g: 30g and 40 kg: 48 kg in proportion?
If x : y = y : z, then x2 : y2 is ______.
