Advertisements
Advertisements
Question
If `a/c = c/d = c/f` prove that : `bd f[(a + b)/b + (c + d)/d + (c + f)/f]^3` = 27(a + b)(c + d)(e + f)
Advertisements
Solution
`a/c = c/d = c/f` = k(say)
∴ a = bk, c = dk, e =fk
L.H.S. = `bd f[(a + b)/b + (c + d)/d + (c + f)/f]^3`
= `bd f[(bk + b)/b + (dk + d)/d + (fk + f)/f]^3`
= `bd f[(b(k + 1))/b + (d(k + 1))/d + (f(k + 1))/f]^3`
= bdf(k + 1 + k + 1 + k + 1)3
= bdf(3k + 3)3 = 27bdf(k + 1)3
R.H.S. = 27(a + b)(c + d)(e + f)
= 27(bk + b)(dk + d)(fk + f)
= 27b(k + 1)d(k + 1)f(k + 1)
= 27bdf(k + 1)3
∴ L.H.S. = R.H.S.
APPEARS IN
RELATED QUESTIONS
Find the mean proportional between `6 + 3sqrt(3)` and `8 - 4sqrt(3)`
If a, b and c are in continued proportion, prove that `(a^2 + b^2 + c^2)/(a + b + c)^2 = (a - b + c)/(a + b + c)`
Which number should be subtracted from 12, 16 and 21 so that resultant numbers are in continued proportion?
If x, 12 and 16 are in continued proportion! find x.
If `x/a = y/b = z/c`, show that `x^3/a^3 - y^3/b^3 = z^3/c^3 = (xyz)/(zbc).`
In a fort, 550 men had provisions for 28 days. How many days will it last for 700 men?
Choose the correct answer from the given options :
If x, 12, 8 and 32 are in proportion, then the value of x is
If a, b, c, d, e are in continued proportion, prove that: a : e = a4 : b4.
7 Persons is to 49 Persons as 11 kg is to 88 kg
Which of the following statements correctly defines a proportion involving four non-zero quantities a, b, c, and d?
