Advertisements
Advertisements
प्रश्न
If a, b, c and dare in continued proportion, then prove that
ad (c2 + d2) = c3 (b + d)
Advertisements
उत्तर
ad (c2 + d2) = c3 (b + d)
`"a"/"b" = "b"/"c" = "c"/"d" = "k"`
⇒ c = kd
b =kc= k2d
a=kb=k3d
ac( c2 + d2 ) = c3(b + d)
LHS
ac( c2 + d2)
= k3d x c(k2 d2 + d2)
= k3d3 (k2d + d)
RHS
c3(b + d)
= k3d3(k2d + d)
LHS = RHS. Hence , proved.
APPEARS IN
संबंधित प्रश्न
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)`
Check whether the following numbers are in continued proportion.
1, 2, 3
If ( a+c) : b = 5 : 1 and (bc + cd) : bd = 5 : 1, then prove that a : b = c : d
Find the fourth proportional to:
x3 - y2, x4 + x2y2 + y4, x - y.
If a, b, c, d are in continued proportion, prove that (b − c)2 + (c − a)2 + (d − b)2 = (d − a)2.
If a : b = c : d, show that (a - c) b2 : (b - d) cd = (a2 - b2 - ab) : (c2 - d2 - cd).
A car travels 195 km in 3 hours.
(i) How long will it take to travel 520 km?
(ii) How far will it travel in 7 hours at the same speed?
If a, b, c and d are in proportion, prove that: `(a^2 + ab)/(c^2 + cd) = (b^2 - 2ab)/(d^2 - 2cd)`
Choose the correct answer from the given options :
The mean proportional between `(1)/(2)` and 128 is
If x + y + z = 0, the value of `x/(y + z)` is ______.
