Advertisements
Advertisements
Question
If a, b, c, d are in continued proportion, prove that:
(a2 + b2 + c2) (b2 + c2 + d2) = (ab + bc + cd)2.
Advertisements
Solution
L.H.S.
= (d2k6 + d2k4 + d2k2)(d2k4 + d2k2 + d2)
= d2k2 (k4 + k2 + 1)d2 (k4 + k2 + 1)
= d4k2 (k4 + k2 + 1)2
R.H.S.
= (ab + bc + cd)2
= (dk3·dk2 + dk2·dk + dk·d)2
= d4·k2 (k4 + k2 + 1)2
L.H.S. = R.H.S.
Hence proved.
RELATED QUESTIONS
Using the properties of proportion, solve for x, given `(x^4 + 1)/(2x^2) = 17/8`.
If x, y, z are in continued proportion prove that `(x + y)^2/(y + z)^2 = x/z`
Find the third proportion to the following :
16x2 and 24x
Find the third proportion to the following :
(x - y) and m (x - y)
If x, 12 and 16 are in continued proportion! find x.
Using the properties of proportion, solve for x, given. `(x^4 + 1)/(2x^2) = (17)/(8)`.
What number should be subtracted from each of the numbers 23, 30, 57 and 78 so that the remainders are in proportion ?
Write (T) for true and (F) for false in case of the following:
36 : 45 : : 80 : 100
Are the ratios 25g: 30g and 40 kg: 48 kg in proportion?
If the weight of 40 books is 8 kg, then the weight of 15 books is 3 kg
