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
If `x = (sqrt(a + 3b) + sqrt(a - 3b))/(sqrt(a + 3b) - sqrt(a - 3b))`, prove that: 3bx2 – 2ax + 3b = 0.
If x, y, z are in continued proportion prove that `(x + y)^2/(y + z)^2 = x/z`
If y is the mean proportional between x and y; show that y(x+z) is the mean p roporti ona I between x2+ y2 and y2+ z2
If a : b = c : d, show that (a - c) b2 : (b - d) cd = (a2 - b2 - ab) : (c2 - d2 - cd).
Find the fourth proportional to `(1)/(3), (1)/(4), (1)/(5)`
Find the mean proportion of: `(1)/(12) and (1)/(75)`
If a, 12, 16 and b are in continued proportion find a and b.
If a, b, c are in continued proportion, prove that: a2 b2 c2 (a-4 + b-4 + c-4) = b-2(a4 + b4 + c4)
10 books is to 15 books as 3 books is to 15 books
The mean proportional between 4 and 9 is ______.
