Advertisements
Advertisements
प्रश्न
If a, b, c and d are in proportion, prove that: `(a + c)^3/(b + d)^3 = (a(a - c)^2)/(b(b - d)^2)`
Advertisements
उत्तर
∵ a, b, c, d are in proportion
`a/b = c/d` = k(say)
a = bk, c = dk.
L.H.S. = `(a + c)^3/(b + d)^3`
= `(bk + dk)^3/(b + d)^3`
= `(k^3(b + d)^3)/(b + d)^2`
= k3
R.H.S. = `(a(a - c)^2)/(b(b - d)^2`
= `(bk(bk - dk)^2)/(b(b - d)^2`
= `(bk.k^2(b - d)^2)/(b(b - d)^2`
= k3
∴ L.H.S. = R.H.S.
APPEARS IN
संबंधित प्रश्न
Find the mean proportional between a – b and a3 – a2b
If y is the mean proportional between x and z, prove that: `(x^2 - y^2 + z^2)/(x^(-2) - y^(-2) + z^(-2)) = y^4`.
If p, q and r in continued proportion, then prove the following:
(p + q + r )(p - q + r) = p2 + q2 + r2
Find the third proportional to:
x - y, x2 - y2
Find the value of x in each of the following proportions:
51 : 85 : : 57 : x
In a fort, 550 men had provisions for 28 days. How many days will it last for 700 men?
If a, b, c and d are in proportion, prove that: (a4 + c4) : (b4 + d4) = a2 c2 : b2 d2.
If a, b, c are in continued proportion, prove that: `(pa^2+ qab+ rb^2)/(pb^2+qbc+rc^2) = a/c`
What number must be added to each of the numbers 15, 17, 34 and 38 to make them proportional?
In the proportional statement p : q :: r : s, which pair of terms represents the means, and which pair represents the extremes?
