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/d`, show that: `(a^3c + ac^3)/(b^3d + bd^3) = (a + c)^4/(b + d)^4`.
If p + r = mq and `1/q + 1/s = m/r`; then prove that p : q = r : s.
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 1.5, 2.5, 4.5
Choose the correct statement:
Choose the correct answer from the given options :
The third proportional to `6(1)/(4)` and 5 is
`square` : 24 : : 3 : 8
A car travels 90 km in 3 hours with constant speed. It will travel 140 km in 5 hours at the same speed
A student said that the ratios `3/4` and `9/16` were proportional. What error did the student make?
If x : y = y : z, then x2 : y2 is ______.
