Advertisements
Advertisements
Question
Using properties of proportion, solve for x. Given that x is positive:
`(2x + sqrt(4x^2 -1))/(2x - sqrt(4x^2 - 1)) = 4`
Solution
`(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`
`=> (4x^2)/(4x^2 -1) = 25/9` (squaring both sides)
`=>(4x^2 - 4x^2 + 1)/(4x^2 -1) = (25-9)/9` (By dividendo)
`=> 1/(4x^2 -1) = 16/9`
`=> 9 = 64x^2 - 16`
`=> 64x^2 = 25`
`=> x^2 = 25/64`
`=> x = +- 5/8`
`=> x = 5/8` (x is positive)
APPEARS IN
RELATED QUESTIONS
If b is the mean proportion between a and c, show that: `(a^4 + a^2b^2 + b^4)/(b^4 + b^2c^2 + c^4) = a^2/c^2`.
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.
Find the third proportion to the following :
16x2 and 24x
If p, q and r in continued proportion, then prove the following:
(p2 - q2)(q2 + r2) = (q2 - r2)(p2 + q2)
If a, b, c and dare in continued proportion, then prove that
(a+ d)(b+ c)-(a+ c)(b+ d)= (b-c)2
If 2x – 1, 5x – 6, 6x + 2 and 15x – 9 are in proportion, find the value of x.
Show that the following numbers are in continued proportion:
16, 84, 441
If 25 : 35 : : 45 : x, then the value of x is
If 40 men can finish a piece of work in 26 days, how many men will be required to finish it in 20 days?
If ax = by = cz; prove that `x^2/"yz" + y^2/"zx" + z^2/"xy" = "bc"/a^2 + "ca"/b^2 + "ab"/c^2`
