Advertisements
Advertisements
प्रश्न
If x and y be unequal and x : y is the duplicate ratio of x + z and y + z, prove that z is mean proportional between x and y.
Advertisements
उत्तर
Given, `x/y = (x + z)^2/(y + z)^2`
`=> x/y = (x^2 + 2xz + z^2)/(y^2 + 2yz + z^2)`
`=> x(y^2 + 2yz + z^2) = y (x^2 + 2xz + z^2)`
`=> xy^2 + 2xyz + xz^2 = x^2y + 2xyz + yz^2`
`=> xy^2 - x^2y = yz^2 - xz^2`
`=> xy(-x + y) = z^2 (y - x)`
`=> z^2 = xy`
`=> x/z = z/y`
APPEARS IN
संबंधित प्रश्न
If three quantities are in continued proportion; show that the ratio of the first to the third is the duplicate ratio of the first to the second.
Check whether the following numbers are in continued proportion.
9, 12, 16
Find the value of the unknown in the following proportion :
5 : 12 :: 15 : x
Find the third proportion to the following :
(x - y) and m (x - y)
What least number must be added to each of the numbers 5, 11, 19 and 37, so that they are in proportion?
Find the fourth proportional to 1.5, 2.5, 4.5
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"`
The length and breadth of a school ground are 150 m and 90 m respectively, while the length and breadth of a mela ground are 210 m and 126 m, respectively. Are these measurements in proportion?
Write True (T) or False (F) against the following statement:
16 : 24 : : 20 : 30
Write True (T) or False (F) against the following statement:
0.9 : 0.36 : : 10 : 4
