Advertisements
Advertisements
प्रश्न
If `x/a = y/b = z/c`, prove that `x^3/a^2 + y^2/b^2 + z^3/c^2 = ((x + y + z)^3)/((a + b ++ c)^2)`.
Advertisements
उत्तर
Let `x/a = y/b = z/c = k` ...[By k method]
x = ak, y = bk and z = ck.
L.H.S.
= `(a^3k^3)/(a^2) + (b^3k^3)/(b^2) + (c^3k^3)/(c^2)`
⇒ k3 [a + b + c]
R.H.S.
= `[ak + bk + ck]^3/[a + b + c]^2`
⇒ `(k^3[a + b + c]^3)/[a + b + c]^2`
= k3 (a + b + c)
L.H.S. = R.H.S.
Hence proved.
APPEARS IN
संबंधित प्रश्न
Find the third proportional to `x/y + y/x` and `sqrt(x^2 + y^2)`
Find the fourth proportional to 2xy, x2 and y2.
If a : b = c : d; then show that (ax+ by) : b = (cx+ dy) : d
If u, v, w, and x are in continued proportion, then prove that (2u+3x) : (3u+4x) : : (2u3+3v3) : (3u3+4v3)
Verify the following:
91 : 104 : : 119 : 136
If the cost of 14 m of cloth is Rs 1890, find the cost of 6 m of cloth.
The angles of a triangle are in the ratio 3 : 1 : 2. The measure of the largest angle is
Sleeping time of a python in a 24 hour clock is represented by the shaded portion in the following figure.
The ratio of sleeping time to awaking time is ______.
The length and breadth of a school ground are 150 m and 90 m respectively, while the length and breadth of a mela ground are 210 m and 126 m, respectively. Are these measurements in proportion?
The mean proportional between 4 and 9 is ______.
