Advertisements
Advertisements
प्रश्न
If a, b, c, d, e are in continued proportion, prove that: a : e = a4 : b4.
Advertisements
उत्तर
a, b, c, d, e are in continued proportion
⇒ `a/b = b/c = c/d = d/c` = k (say)
d = ek, c = ek2, b = ek3 and a = ek4
Now L.H.S. = `a/e`
= `(ek^4)/e`
= k4
R.H.S. `a^4/b^4`
= `(ek^4)^4/(ek^3)^4`
= `(e^4k^16)/(e^4k^12)`
= k16-12
= k4
∴ L.H.S. = R.H.S.
APPEARS IN
संबंधित प्रश्न
What least number must be subtracted from each of the numbers 7, 17 and 47 so that the remainders are in continued proportion?
If a, b, c and d are in proportion prove that `sqrt((4a^2 + 9b^2)/(4c^2 + 9d^2)) = ((xa^3 - 4yb^3)/(xc^3 - 5yd^3))^(1/3)`
If p, q and r in continued proportion, then prove the following:
(p + q + r )(p - q + r) = p2 + q2 + r2
Find the fourth proportional to 3, 12, 15
If a, b, c and d are in proportion, prove that: (a4 + c4) : (b4 + d4) = a2 c2 : b2 d2.
If a, b, c and d are in proportion, prove that: `(a^2 + b^2)/(c^2 + d^2) = "ab + ad - bc"/"bc + cd - ad"`
There is a number in the box `square` such that `square`, 24, 9, 12 are in proportion. The number in the box is ______.
Determine if the following are in proportion.
33, 44, 75, 100
If `(a + b)^3/(a - b)^3 = 64/27`
- Find `(a + b)/(a - b)`
- Hence using properties of proportion, find a : b.
If x : y = y : z, then x2 : y2 is ______.
