Advertisements
Advertisements
Question
If x, y, z are in continued proportion, prove that `(x + y)^2/(y + z)^2 = x/z`
Advertisements
Solution
∵ x,y,z are in continued proportion,
`∴ x/y = y/z => y^2 = zx .....(1)`
`(x + y)/y = (y + z)/z` (By componendo)
`=> (x + y)^2/(y + z) = y/z` (By alternendo)
`=> (x + y)^2/(y + z)^2 = y^2/z^2 => (x + y)^2/(y + z)^2 = (zx)/z^2`
`=> (x + y)^2/(y + z)^2 = x/z `
Hence Proved
APPEARS IN
RELATED QUESTIONS
What least number must be added to each of the numbers 16, 7, 79 and 43 so that the resulting
numbers are in proportion?
Which number should be subtracted from 12, 16 and 21 so that resultant numbers are in continued proportion?
Check whether the following numbers are in continued proportion.
9, 12, 16
Find the fourth proportion to the following:
0.7, 4.9 and 1.6
Given four quantities p, q, r and s are in proportion, show that
q2(p - r) : rs (q - s) =(p2- q2- pq): ( r2-s2-rs).
Find the two numbers such that their mean proprtional is 24 and the third proportinal is 1,536.
Write (T) for true and (F) for false in case of the following:
32 kg : Rs 36 : : 8 kg : Rs 9
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)`
Are 30, 40, 45, and 60 in proportion?
If two ratios are equal, then they are in ______.
