Advertisements
Advertisements
प्रश्न
If `(x^3 + 3xy^2)/(3x^2y + y^3) = (m^3 + 3mn^2)/(3m^2n + n^3)`, show that nx = my.
उत्तर
`(x^3 + 3xy^2)/(3x^2y + y^3) = (m^3 + 3mn^2)/(3m^2n + n^3)`
Applying componendo and dividendo,
`(x^3 + 3xy^2 + 3x^2y + y^3)/(x^3 + 3xy^2 - 3x^2y - y^3) = (m^3 + 3mn^2 + 3m^2n + n^3)/(m^3 + 3mn^2 - 3m^2n - n^3)`
`(x + y)^3/(x - y)^3 = (m + n)^3/(m - n)^3`
`(x + y)/(x - y) = (m + n)/(m - n)`
Applying componendo and dividendo,
`(x + y + x - y)/(x + y - x + y) = (m + n + m - n)/(m + n - m + n)`
`(2x)/(2y) = (2m)/(2n)`
`x/y = m/n`
nx = my
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: (6a + 7b)(3c – 4d) = (6c + 7d)(3a – 4b).
If `(7"a" + 12"b")/(7"c" + 12"d")` then prove that `"a"/"b"="c"/"d"`
If a : b :: c : d :: e : f, then prove that `("ae" + "bf")/("ae" - "bf")` = `("ce" + "df")/("ce" - "df")`
If (a + 3b + 2c + 6d) (a – 3b – 2c + 6d) = (a + 3b – 2c – 6d) (a – 3b + 2c – 6d), 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)`
If x = `(2mab)/(a + b)`, find the value of `(x + ma)/(x - ma) + (x + mb)/(x - mb)`
If x = `(root(3)(a + 1) + root(3)(a - 1))/(root(3)(a + 1) - root(3)(a - 1)`,prove that :
x³ – 3ax² + 3x – a = 0
If `(x^2 - 1)/(x^2 + 1) = 3/5`, the value of x is ______.
If (m + n) : (n – m) = 5 : 2 ; m : n is ______.
