Advertisements
Advertisements
Question
If a, b, c are in continued proportion, prove that: abc(a + b + c)3 = (ab + bc + ca)3
Advertisements
Solution
As a, b, c, are in continued proportion
Let `a/b = b/c` = k
L.H.S. = abc(a + b + c)3
= ck2.ck.c[ck2 + ck + c]3
= c3k3[c(k2 + k + 1)]3
= c3k3.c3.(k2 + k + 1)3
= c6k3(k2 + k + 1)3
R.H.S. = (ab + bc + ca)3
= (ck2.ck + ck.c + c. ck2)3
= (c2k3 + c2k + c2k2)3
= (c2k3 + c2k2 + c2k)3
= [c2k(k2 + k + 1)]3
= c6k3(k + k + 1)3
∴ L.H.S. = R.H.S.
APPEARS IN
RELATED QUESTIONS
Find the mean proportional to (x – y) and (x3 – x2y).
Find the value of the unknown in the following proportion :
3 : 4 : : p : 12
Find the third proportion to the following :
(x - y) and m (x - y)
Find the mean proportion of the following :
24 and 6
Using the properties of proportion, solve for x, given. `(x^4 + 1)/(2x^2) = (17)/(8)`.
What number must be added to each of the numbers 5, 11, 19 and 37 so that they are in proportion?
Write (T) for true and (F) for false in case of the following:
81 kg : 45 kg : : 18 men : 10 men
If Rs 760 is divided between A and B in the ratio 8 : 11, then B's share is
If a, b, c and d are in proportion, prove that: `(a^2 + ab + b^2)/(a^2 - ab + b^2) = (c^2 + cd + d^2)/(c^2 - cd + d^2)`
Find the missing number in the box in the proportions:
`3/8 = square/20`
