Advertisements
Advertisements
Question
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)`
Solution
Given, a, b and c are in continued proportion.
Therefore,
`a/b = b/c`
ac = b2
L.H.S = `(a^2 + b^2 + c^2)/(a + b + c)^2`
= `(a^2 + b^2 + c^2 + 2ab + 2bc + 2ac - (2ab + 2bc + 2ac))/((a + b + c)^2)`
= `((a + b + c)^2 - 2(ab + bc + b^2))/((a + b + c)^2)`
= `((a + b + c)^2 - 2b(a + c + b))/((a + b + c)^2)`
= `((a + b + c)(a + b + c - 2b))/((a + b + c)^2)`
= `(a - b + c)/(a + b + c)`
Hence proved.
APPEARS IN
RELATED QUESTIONS
If a, b, c are in continued proportion and a(b - c) = 2b, prove that `a - c = (2(a + b))/a`
If a, b and c are in continued proportion, prove that: a: c = (a2 + b2) : (b2 + c2)
If x, y, z are in continued proportion prove that `(x + y)^2/(y + z)^2 = x/z`
If `a = (b + c)/(2), c = (a + b)/(2)` and b is mean proportional between a and c, prove that `(1)/a + (1)/c = (1)/b`.
Write (T) for true and (F) for false in case of the following:
30 bags : 18 bags : : Rs 450 : Rs 270
In an army camp, there were provisions for 550 men for 28 days. But, 700 men attended the camp. How long did the provisions last?
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"`
If a, b, c and d are in proportion, prove that: `abcd [(1/a^2 + 1/b^2 + 1/c^2 + 1/d^2]` = a2 + b2 + c2 + d2
Determine if the following are in proportion.
33, 121, 9, 96
Determine if the following are in proportion.
4, 6, 8, 12
