Advertisements
Advertisements
प्रश्न
If a, b, c are in continued proportion, prove that a : c = (a2 + b2) : (b2 + c2).
Advertisements
उत्तर
a, b and c are the continued proportion
a: b = b: c
⇒ `a/b = b/c`
⇒ b2 = ac
Now `a/c = (a^2 + b^2)/(b^2 + c^2)`
= a(b2 + c2) = c(a2 + b2)
L.H.S.
⇒ a(b2 + c2)
⇒ a(ac + c2)
⇒ ac(a + c)
R.H.S.
⇒ c(a2 + b2)
⇒ c(a2 + ac)
⇒ ac(a + c)
L.H.S. = R.H.S.
Hence proved.
संबंधित प्रश्न
If a/b = c/d prove that each of the given ratio is equal to `(13a - 8c)/(13b - 8d)`
Find the fourth proportion to the following:
(p2q - qr2 ), (pqr - pr2 ) and (pq2 - pr2)
If p, q and r in continued proportion, then prove the following:
(p + q + r )(p - q + r) = p2 + q2 + r2
If `a = (b + c)/(2), c = (a + b)/(2)` and b is mean proportional between a and c, prove that `(1)/a + (1)/c = (1)/b`.
Find the fourth proportional to 3, 12, 15
What number should be subtracted from each of the numbers 23, 30, 57 and 78 so that the remainders are in proportion ?
Choose the correct answer from the given options :
The mean proportional between `(1)/(2)` and 128 is
Do the ratios 15 cm to 2 m and 10 sec to 3 minutes form a proportion?
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 ratios form a proportion. Also, write the middle terms and extreme terms where the ratios form a proportion.
25 cm : 1 m and ₹ 40 : ₹ 160
