Advertisements
Advertisements
प्रश्न
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)`
Advertisements
उत्तर
∵ a, b, c, d are in proportion
`a/b = c/d` = k(say)
a = bk, c = dk.
L.H.S. = `(a + c)^3/(b + d)^3`
= `(bk + dk)^3/(b + d)^3`
= `(k^3(b + d)^3)/(b + d)^2`
= k3
R.H.S. = `(a(a - c)^2)/(b(b - d)^2`
= `(bk(bk - dk)^2)/(b(b - d)^2`
= `(bk.k^2(b - d)^2)/(b(b - d)^2`
= k3
∴ L.H.S. = R.H.S.
APPEARS IN
संबंधित प्रश्न
If a/b = c/d prove that each of the given ratio is equal to `(13a - 8c)/(13b - 8d)`
If a/b = c/d prove that each of the given ratio is equal to `sqrt((3a^2 - 10c^2)/(3b^2 - 10d^2))`
If a, b, c and d are in proportion prove that `(13a + 17b)/(13c + 17d) = sqrt((2ma^2 - 3nb^2)/(2mc^2 - 3nd^2)`
Find the smallest number that must be subtracted from each of the numbers 20, 29, 84 and 129 so that they are in proportion.
Find the value of x in the following proportions : 3 : x = 24 : 2
If a, 12, 16 and b are in continued proportion find a and b.
Determine if the following numbers are in proportion:
32, 48, 70, 210
If a, b, c are in continued proportion, prove that: `(1)/a^3 + (1)/b^3 + (1)/c^3 = a/(b^2c^2) + b/(c^2a^2) + c/(a^2b^2)`
If a, b, c, d are in continued proportion, prove that: a : d = triplicate ratio of (a – b) : (b – c)
If 2x, 9 and 18 are in continued proportion, the value of x is ______.
