Advertisements
Advertisements
प्रश्न
If `x = (2ab)/(a + b)`, find the value of `(x + a)/(x - a) + (x +b)/(x - b)`.
उत्तर
`x = (2ab)/(a + b)`
`x/a = (2b)/(a + b)`
Applying componendo and dividendo,
`(x + a)/(x - a) = (2b + a + b)/(2b - a - b)`
`(x + a)/(x - a) = (3b + a)/(b - a)` ...(1)
Also, `x = (2ab)/(a + b)`
Applying componendo and dividendo,
`(x + b)/(x - b) = (2a + a + b)/(2a - a - b)`
`(x + b)/(x - b) = (3a + a)/(a - b)` ...(2)
From (1) and (2)
`(x + a)/(x - a) + (x + b)/(x - b) = (3b + a)/(b - a) + (3a + b)/(a - b)`
`(x + a)/(x - a) + (x + b)/(x - b) = (-3b - a + 3a + b)/(a - b)`
`(x + a)/(x - a) + (x + b)/(x - b) = (2a - 2b)/(a - b) = 2`
APPEARS IN
संबंधित प्रश्न
Given that `(a^3 + 3ab^2)/(b^2 + 3a^2b) = (63)/(62)`.
Using Componendo and Dividendo find a : b.
If `(3x + 5y)/(3x - 5y) = (7)/(3)`, find x : y.
Solve for x : `(1 - px)/(1 + px) = sqrt((1 + qx)/(1 - qx)`
if `(3a + 4b)/(3c + 4d) = (3a - 4b)/(3c - 4d)` Prove that `a/b = c/d`.
If x = `(4sqrt(6))/(sqrt(2) + sqrt(3)` find the value of `(x + 2sqrt(2))/(x - 2sqrt(2)) + (x + 2sqrt(3))/(x - 2sqrt(3)`
Solve x : `(sqrt(36x + 1) + 6sqrt(x))/(sqrt(36x + 1) -6sqrt(x))` = 9
If x = `(sqrt(a + 1) + sqrt(a - 1))/(sqrt(a + 1 - sqrt(a - 1)`, using properties of proportion, show that x2 – 2ax + 1 = 0
Given that `(a^3 + 3ab^2)/(b^3 + 3a^2b) = (63)/(62)`. Using componendo and dividendo find a: b.
Using Componendo and Dividendo solve for x:
`(sqrt(2x + 2) + sqrt(2x - 1))/(sqrt(2x + 2) - sqrt(2x - 1))` = 3
If x = y, the value of (3x + y) : (5x – 3y) is ______.
