Advertisements
Advertisements
प्रश्न
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)`
उत्तर
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
संबंधित प्रश्न
Find the mean proportion of the following :
`28/3` and `175/27`
Find the value of x in the following proportions : x : 50 :: 3 : 2
If the cost of 14 m of cloth is Rs 1890, find the cost of 6 m of cloth.
A transport company charges Rs 540 to carry 25 tonnes of weight. What will it charge to carry 35 tonnes?
If 25 : 35 : : 45 : x, then the value of x is
If `x/a = y/b = z/c`, prove that `x^3/a^2 + y^3/b^2 + z^3/c^2 = (x+ y+ z)^3/(a + b+ c)^2`
If a, b, c and d are in proportion, prove that: `(a^2 + b^2)/(c^2 + d^2) = "ab + ad - bc"/"bc + cd - ad"`
If a, b, c are in continued proportion, prove that: (a + b + c) (a – b + c) = a2 + b2 + c2
A gets double of what B gets and B gets double of what C gets. Find A : B and B : C and verify whether the result is in proportion or not
If x + y + z = 0, the value of `x/(y + z)` is ______.
