Advertisements
Advertisements
प्रश्न
If `a/b = c/d`, show that: `(a^3c + ac^3)/(b^3d + bd^3) = (a + c)^4/(b + d)^4`.
Advertisements
उत्तर
Let `a/b = c/d = k`
`=>` a = bk and c = dk
L.H.S = `(a^3c + ac^3)/(b^3d + bd^3)`
= `(ac(a^2 + c^2))/(bd(b^2 + d^2))`
= `((bk xx dk)(b^2k^2 + d^2k^2))/(bd(b^2 + d^2))`
= `(k^2 xx k^2(b^2 + d^2))/(b^2 + d^2)`
= k4
R.H.S = `(a + c)^4/(b + d)^4`
= `(bk + dk)^4/(b + d)^4`
= `[(k(b + d))/(b + d)]^4`
= k4
Hence `(a^3c + ac^3)/(b^3d + bd^3) = (a + c)^4/(b + d)^4`
APPEARS IN
संबंधित प्रश्न
6 is the mean proportion between two numbers x and y and 48 is the third proportional of x and y. Find the numbers.
Using properties of proportion, solve for x:
`(sqrt(x + 1) + sqrt(x - 1))/(sqrt(x + 1) - sqrt(x - 1)) = (4x - 1)/2`
If a, b, c, d are in continued proportion, prove that (b − c)2 + (c − a)2 + (d − b)2 = (d − a)2.
Find the value of x in the following proportions : 10 : 35 = x : 42
The cost of 18 chairs is Rs 22770. How many such chairs can be bought for Rs 10120?
If a, b, c, d are in proportion, then
If ax = by = cz; prove that `x^2/"yz" + y^2/"zx" + z^2/"xy" = "bc"/a^2 + "ca"/b^2 + "ab"/c^2`
Determine if the following are in proportion.
33, 121, 9, 96
Write True (T) or False (F) against the following statement:
5.2 : 3.9 : : 3 : 4
What is the term "d" called in the expression a : b :: c : d?
