Advertisements
Advertisements
प्रश्न
If a, b, c are in continued proportion, show that: `(a^2 + b^2)/(b(a + c)) = (b(a + c))/(b^2 + c^2)`.
Advertisements
उत्तर
Since a, b, c are in continued proportion,
`a/b = b/c`
`=>` b2 = ac
Now, (a2 + b2)(b2 + c2) = (a2 + ac)(ac + c2)
= a(a + c) c(a + c)
= ac(a + c)2
= b2(a + c)2
`=>` (a2 + b2)(b2 + c2) = [b(a + c)][b(a + c)]
`=> (a^2 + b^2)/(b(a + c)) = (b(a + c))/(b^2 + c^2)`
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, show that (a - c) b2 : (b - d) cd = (a2 - b2 - ab) : (c2 - d2 - cd).
What number should be subtracted from each of the numbers 23, 30, 57 and 78 so that the remainders are in proportion ?
What number must be added to each of the numbers 16, 26 and 40 so that the resulting numbers may be in continued proportion?
Write (T) for true and (F) for false in case of the following:
36 : 45 : : 80 : 100
If 9, x, x 49 are in proportion, find the value of x.
If the cost of 14 m of cloth is Rs 1890, find the cost of 6 m of cloth.
If a, b, c and d are in proportion, prove that: `(a^2 + ab)/(c^2 + cd) = (b^2 - 2ab)/(d^2 - 2cd)`
Sleeping time of a python in a 24 hour clock is represented by the shaded portion in the following figure.
The ratio of sleeping time to awaking time is ______.
Determine if the following are in proportion.
32, 48, 70, 210
