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 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.
If p, q and r in continued proportion, then prove the following:
(p + q + r )(p - q + r) = p2 + q2 + r2
An electric pole casts a shadow of length 20 m at a time when a tree 6 m high casts a shadow of length 8 m. Find the height of the pole.
35 inland letters cost Rs 87.50. How many such letters can we buy for 315?
If 24 workers can build a wall in 15 days, how many days will 8 workers take to build a similar wall?
If a, b, c are in continued proportion, prove that: `(pa^2+ qab+ rb^2)/(pb^2+qbc+rc^2) = a/c`
If a, b, c are in continued proportion, prove that: a2 b2 c2 (a-4 + b-4 + c-4) = b-2(a4 + b4 + c4)
Write True (T) or False (F) against the following statement:
8 : 9 : : 24 : 27
If x, 2, 10 and y are in continued proportion, the values of x and y are respectively:
Which of the following statements correctly defines a proportion involving four non-zero quantities a, b, c, and d?
