Advertisements
Advertisements
प्रश्न
Using properties of proportion, solve for x:
`(sqrt(x + 1) + sqrt(x - 1))/(sqrt(x + 1) - sqrt(x - 1)) = (4x - 1)/2`
Advertisements
उत्तर
`(sqrt(x + 1) + sqrt(x - 1))/(sqrt(x + 1) - sqrt(x - 1)) = (4x - 1)/2`
Applying componendo and dividendo,
`(sqrt(x + 1) + sqrt(x - 1) + sqrt(x + 1) - sqrt(x - 1))/(sqrt(x + 1) + sqrt(x - 1) - sqrt(x + 1) + sqrt(x - 1)) = (4x - 1 + 2)/(4x - 1 - 2)`
`(2sqrt(x + 1))/(2sqrt(x - 1)) = (4x + 1)/(4x - 3 )`
Squaring both sides,
`(x + 1)/(x - 1) = (16x^2 + 1 + 8x )/(16x^2 + 9 - 24x)`
Applying componendo and dividendo,
`(x + 1 + x - 1)/(x + 1 - x + 1) = (16x^2 + 1 + 8x + 16x^2 + 9 - 24x)/(16x^2 + 1 + 8x - 16x^2 - 9 + 24x)`
`(2x)/2 = (32x^2 + 10 - 16x )/(32x - 8)`
`x = (16x^2 + 5 - 8x)/(16x - 4)`
16x2 – 4x = 16x2 + 5 – 8x
4x = 5
`x = 5/4`
APPEARS IN
संबंधित प्रश्न
6 is the mean proportion between two numbers x and y and 48 is the third proportional of x and y. Find the numbers.
If a, b, c are in continued proportion, show that: `(a^2 + b^2)/(b(a + c)) = (b(a + c))/(b^2 + c^2)`.
If p : q = r : s; then show that: mp + nq : q = mr + ns : s.
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.
If `a/b = c/d = r/f`, prove that `((a^2b^2 + c^2d^2 + e^2f^2)/(ab^3 + cd^3 + ef^3))^(3/2) = sqrt((ace)/(bdf)`
Find the value of x in the following proportions : 2.5 : 1.5 = x : 3
If 40 men can finish a piece of work in 26 days, how many men will be required to finish it in 20 days?
The length and breadth of a rectangular field are in the ratio 5 : 4. If the width of the field is 36 m, what is its length?
If `a/c = c/d = c/f` prove that : `bd f[(a + b)/b + (c + d)/d + (c + f)/f]^3` = 27(a + b)(c + d)(e + f)
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?
