Advertisements
Advertisements
प्रश्न
If `a/b = c/d = e/f`, prove that `(ab + cd + ef)^2 = (a^2 + c^2 + e^2) (b^2 + d^2 + f^2)`.
Advertisements
उत्तर
Let `a/b = c/d = e/f = k` then
a = bk, c = dk and e = fk
L.H.S.
= (ab + cd + ef)2
= (bk·b + dk·d + fk·f)2
= k2 (b2 + d2 + f2)2
R.H.S.
= (a2 + c2 + e2)(b2 + d2 + f2)
= (b2k2 + d2k2 + f2k2)(b2 + d2 + f2)
= k2 (b2 + d2 + f2)(b2 + d2 + f2)
= k2 (b2 + d2 + f2)2.
L.H.S. = R.H.S.
Hence proved.
संबंधित प्रश्न
If q is the mean proportional between p and r, show that: pqr(p + q + r)3 = (pq + qr + rp)3.
If `x = (sqrt(a + 3b) + sqrt(a - 3b))/(sqrt(a + 3b) - sqrt(a - 3b))`, prove that: 3bx2 – 2ax + 3b = 0.
Find the mean proportion of the following :
`28/3` and `175/27`
Find the third proportional to:
`a/b + b/c, sqrt(a^2 + b^2)`.
Find the two numbers such that their mean proprtional is 24 and the third proportinal is 1,536.
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)`.
Find the third proportional to Rs. 3, Rs. 12
Determine if the following numbers are in proportion:
7, 42, 13, 78
Show that the following numbers are in continued proportion:
36, 90, 225
If a, b, c and d are in proportion, prove that: `abcd [(1/a^2 + 1/b^2 + 1/c^2 + 1/d^2]` = a2 + b2 + c2 + d2
