Advertisements
Advertisements
प्रश्न
If a : b : : c : d, prove that (la + mb) : (lc + mb) :: (la – mb) : (lc – mb)
उत्तर
∵ a : b :: c : d
∴ `a/b = c/d`
⇒ `"la"/"mb" = "lc"/"md" ...("Multiply by" "l"/"m")`
Applying componendo and dividendo,
`"la + mb"/"la - mb" = "lc + md"/"lc - md"`
⇒ `"la + mb"/"lc + md" = "la - mb"/"lc - md"` ...(By alternendo)
⇒ (la + mb) : (lc + md) :: (la – mb) : (lc – md).
APPEARS IN
संबंधित प्रश्न
If `(7m + 2n)/(7m - 2n) = 5/3`, use properties of proportion to find:
- m : n
- `(m^2 + n^2)/(m^2 - n^2)`
If a : b = c : d, prove that: (9a + 13b)(9c – 13d) = (9c + 13d)(9a – 13b).
Using the properties of proportion solve for x given `(x^4 + 1)/(2x^2) = 17/8`
Given x = `(sqrt(a^2 + b^2) + sqrt(a^2 - b^2))/(sqrt(a^2 + b^2) + sqrt(a^2 - b^2))`
Use componendo and dividendo to prove that b^2 = (2a^2x)/(x^2 + 1)
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 `(x^3 + 12x)/(6x^2 + 8) = (y^3 + 27y)/(9y^2 + 27)` using componendo and divendo find x : y
If a : b = c : d, show that (2a - 7b) (2c + 7d) = (2c - 7d) (2a + 7b).
Find x from the following equations : `(sqrt(2 - x) + sqrt(2 + x))/(sqrt(2 - x) - sqrt(2 + x)` = 3
Find x from the following equations : `(sqrt(x + 4) + sqrt(x - 10))/(sqrt(x + 4) - sqrt(x - 10)) = (5)/(2)`
If x = `"pab"/(a + b)`, provee that `(x + pa)/(x - pa) - (x + pb)/(x - pb) = (2(a^2 - b^2))/(ab)`
