Advertisements
Advertisements
Question
If `a/c = c/d = c/f` prove that : `(a^2)/(b^2) + (c^2)/(d^2) + (e^2)/(f^2) = "ac"/"bd" + "ce"/"df" + "ae"/"df"`
Advertisements
Solution
`a/c = c/d = c/f` = k(say)
∴ a = bk, c = dk, e =fk
L.H.S. = `(a^2)/(b^2) + (c^2)/(d^2) + (e^2)/(f^2)`
= `(b^2k^2)/(b^2) + (d^2k^2)/(d^2) + (f^2k^2)/(f^2)`
= k2 + k2 + k2
= 3k2
R.H.S. = `"ac"/"bd" + "ce"/"df" + "ae"/"bf"`
= `"bk.dk"/"b.d" + "dk.fk"/"d.f" + "bk.fk"/"b.f"`
= k2 + k2 + k2
= 3k2
∴ L.H.S. = R.H.S.
APPEARS IN
RELATED QUESTIONS
if `a/b = c/d` prove that each of the given ratio is equal to: `((8a^3 + 15c^3)/(8b^3 + 15d^3))^(1/3)`
Find the mean proportional of the following:
17.5, 0.007
If x, 12 and 16 are in continued proportion! find x.
Find two numbers whose mean proportional is 18 and the third proportional is 486.
What quantity must be added to each term of the ratio a + b: a - b to make it equal to (a + b)2 : (a - b)2 ?
Find the mean proportion of: 5 and 80
The weight of 65 books is 13 kg.
(i) What is the weight of 80 such books?
(ii) How many such books weigh 6.4 kg?
If a, b, c are in continued proportion, prove that: `(1)/a^3 + (1)/b^3 + (1)/c^3 = a/(b^2c^2) + b/(c^2a^2) + c/(a^2b^2)`
Find two numbers whose mean proportional is 16 and the third proportional is 128.
Find the missing number in the box in the proportions:
`3/8 = square/20`
