Advertisements
Advertisements
प्रश्न
If a : b = c : d, show that (a - c) b2 : (b - d) cd = (a2 - b2 - ab) : (c2 - d2 - cd).
Advertisements
उत्तर
Let `a/b = c/d = k`
⇒ a = bk and c = dk
L.H.S.
= `((a - c)b^2)/((b - d) cd) = ((bk - dk) b^2)/((b - d) dk.d)`
= `(b^2k (b -d))/(d2k (b -d)) = b^2/d^2`
R.H.S.
= `(a^2 - b^2 - ab)/(c^2 - d^2 - cd)`
= `(b^2k^2 - b^2 - bk·b)/(d^2k^2 - d^2 - dk·d)`
= `(b^2 (k^2 - k - 1))/(d^2 (k^2 - k - 1)`
= `b^2/d^2`
L.H.S. = R.H.S.
Hence proved.
APPEARS IN
संबंधित प्रश्न
If a, b, c are in continued proportion and a(b - c) = 2b, prove that `a - c = (2(a + b))/a`
What least number must be subtracted from each of the numbers 7, 17 and 47 so that the remainders are in continued proportion?
Using the properties of proportion, solve for x, given. `(x^4 + 1)/(2x^2) = (17)/(8)`.
If a, b, c, d are in continued proportion, prove that (b − c)2 + (c − a)2 + (d − b)2 = (d − a)2.
Show that the following numbers are in continued proportion:
48, 60, 75
If a, b, c are in proportion, then
Do the ratios 15 cm to 2 m and 10 sec to 3 minutes form a proportion?
Are 30, 40, 45, and 60 in proportion?
The table, given below, shows the values of x and y, where x is proportional (directly proportional) to y.
| x | A | 24 | 15 |
| y | 12 | B | 20 |
The values of A and B are:
The first, third, and fourth terms of a proportion are 9, 24, and 32. Find the second term.
