Advertisements
Advertisements
प्रश्न
If a : b : : c : d, then prove that
`(4"a" + 9"b")/(4"c" + 9"d") = (4"a" - 9"b")/(4"c" - 9"d")`
उत्तर
`(4"a" + 9"b")/(4"c" + 9"d") = (4"a" - 9"b")/(4"c" - 9"d")`
`"a"/"b" = "c"/"d"`
Multiplying both sides by `4/9`
`=> "a"/"b" xx 4/9 = "c"/"d" xx 4/9`
`=> (4"a")/(9"b") = (4"c")/(9"d")`
Applying componendo and dividendo,
`(4"a" + 9"b")/(4"a" - 9"b") = (4"c" + 9"d")/(4"c" - 9"d")`
`=> (4"a" + 9"b")/(4"c" + 9"d") = (4"a" - 9"b")/(4"c" - 9"d")`
Hence, 4a + 9b : 4c + 9d = 4a - 9b : 4c - 9d
APPEARS IN
संबंधित प्रश्न
if x = `(sqrt(a + 1) + sqrt(a-1))/(sqrt(a + 1) - sqrt(a - 1))` using properties of proportion show that `x^2 - 2ax + 1 = 0`
If `(a - 2b - 3c + 4d)/(a + 2b - 3c - 4d) = (a - 2b + 3c - 4d)/(a + 2b + 3c + 4d)`, show that: 2ad = 3bc.
If `(x^2 + y^2)/(x^2 - y^2) = 2 1/8`, find: `(x^3 + y^3)/(x^3 - y^3)`
If a : b :: c : d :: e : f, then prove that `("ae" + "bf")/("ae" - "bf")` = `("ce" + "df")/("ce" - "df")`
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 = `(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
Find x from the following equations : `(sqrt(x + 4) + sqrt(x - 10))/(sqrt(x + 4) - sqrt(x - 10)) = (5)/(2)`
If `(x + y)/(ax + by) = (y + z)/(ay + bz) = (z + x)/(az + bx)`, prove that each of these ratio is equal to `(2)/(a + b)` unless x + y + z = 0
If a : b = 2 : 1, the value of (7a + 4b) : (5a – 2b) is ______.
