Advertisements
Advertisements
प्रश्न
Using properties of proportion, solve for x. Given that x is positive:
`(2x + sqrt(4x^2 -1))/(2x - sqrt(4x^2 - 1)) = 4`
Using properties of proportion, find the value of x from the following:
`(2x + sqrt(4x^2 -1))/(2x - sqrt(4x^2 - 1)) = 4`
Advertisements
उत्तर
`(2x + sqrt(4x^2 -1))/(2x - sqrt(4x^2 - 1)) = 4`
⇒ `(2x + sqrt(4x^2 -1) + 2x - sqrt(4x^2 - 1))/(2x + sqrt(4x^2 - 1) - 2x + sqrt(4x^2 - 1)) = (4+1)/(4-1) ` (By componendo dividendo)
⇒ `(4x)/(2sqrt(4x^2 -1)) = 5/3`
⇒ `(2x)/(sqrt(4x^2 -1)) = 5/3`
Squaring both sides,
⇒ `((2x)/sqrt(4x^2 - 1))^2 = (5/3)^2`
⇒ `(4x^2)/(4x^2 -1) = 25/9`
⇒ 9(4x2) = 25(4x2 − 1)
⇒ 36x2 = 100x2 − 25
⇒ 64x2 = 25
⇒ x2 = `25/64`
⇒ x = `5/8`
APPEARS IN
संबंधित 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)`
Using properties of proportion, solve for x:
`(sqrt(x + 5) + sqrt(x - 16))/(sqrt(x + 5) - sqrt(x - 16)) = 7/3`
If u, v, w, and x are in continued proportion, then prove that (2u+3x) : (3u+4x) : : (2u3+3v3) : (3u3+4v3)
`("pqr")^2 (1/"p"^4 + 1/"q"^4 + 1/"r"^4) = ("p"^4 + "q"^4 + "r"^4)/"q"^2`
If a, b, c and dare in continued proportion, then prove that
ad (c2 + d2) = c3 (b + d)
Find the value of x in each of the following proportion:
27 : x : : 63 : 84
Find the value of x in each of the following proportions:
x : 92 : : 87 : 116
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 57 : x : : 51 : 85, then the value of x is
If (a + 2 b + c), (a – c) and (a – 2 b + c) are in continued proportion, prove that b is the mean proportional between a and c.
The first, third, and fourth terms of a proportion are 9, 24, and 32. Find the second term.
