Advertisements
Advertisements
Question
If `a/c = c/d = c/f` prove that : (b2 + d2 + f2) (a2 + c2 + e2) = (ab + cd + ef)2
Advertisements
Solution
`a/c = c/d = c/f` = k(say)
∴ a = bk, c = dk, e = fk
L.H.S. = (b2 + d2 + f2) (a2 + c2 + e2)
= (b2 + d2 + f2) (b2 k2 + d2 k2 + f2 k2)
= k2 (b2 + d2 + f2) k2 (b2 + d2 + f2)
= k2 (b2 + d2 + f2)2
R.H.S. = (ab + cd + ef)2
= (b. kb + dk. d + fk. f)2
= (kb2 + kd2 + kf2)
= k2 (b2 + d2 + f2)2
∴ L.H.S. = R.H.S.
APPEARS IN
RELATED QUESTIONS
Using properties of proportion, solve for x:
`(sqrt(x + 5) + sqrt(x - 16))/(sqrt(x + 5) - sqrt(x - 16)) = 7/3`
Find the value of the unknown in the following proportion :
3 : 4 : : p : 12
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)
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 : x : 50 :: 3 : 2
Write (T) for true and (F) for false in case of the following:
32 kg : Rs 36 : : 8 kg : Rs 9
If 25 : 35 : : 45 : x, then the value of x is
If the ratios formed using the numbers 2, 5, x, 20 in the same order are in proportion, then ‘x’ is
Determine if the following are in proportion.
15, 45, 40, 120
