Advertisements
Advertisements
प्रश्न
If a : b =c : d, then prove that `("a"^2 + "c"^2)/("b"^2 + "d"^2) = ("ac")/("bc")`
उत्तर
`"a"/"b" = "c"/"d" => "a" = "bc"/"d"`
To prove,
`("a"^2 + "c"^2)/("b"^2 + "d"^2) = ("ac")/("bd")`
LHS
`("a"^2 + "c"^2)/("b"^2 + "d"^2) `
`=(("bc"/"d")^2 + "c"^2)/("b"^2 + "d"^2)`
`= (("b"^2"c"^2)/"d"^2 + "c"^2)/("b"^2 + "d"^2)`
`= ("c"^2 ("b"^2 + "d"^2))/("d"^2("b"^2 + "d"^2))`
`= "c"^2/"d"^2`
RHS
`("ac")/("bd")`
`= (("bc")/"d" "c")/("bd")`
`="bc"^2/"bd"^2`
`= "c"^2/"d"^2`
LHS = RHS
APPEARS IN
संबंधित प्रश्न
If `x = (6ab)/(a + b)`, find the value of `(x + 3a)/(x - 3a) + (x + 3b)/(x - 3b)`.
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 a : b : : c : d, then prove that
`(4"a" + 9"b")/(4"c" + 9"d") = (4"a" - 9"b")/(4"c" - 9"d")`
If a : b : : c : d, prove that `(2a +5b)/(2a - 5b) = (2c + 5d)/(2c - 5d)`
If (pa + qb) : (pc + qd) :: (pa – qb) : (pc – qd) prove that a : b : : c : d
If x = `(8ab)/"a + b"` find the value of `(x + 4a)/(x - 4a) + (x + 4b)/(x - 4b)`
Give `(x^3 + 12x)/(6x^2 + 8) = (y^3 + 27y)/(9y^2 + 27)` Using componendo and dividendo find x : y.
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 x = `(2mab)/(a + b)`, find the value of `(x + ma)/(x - ma) + (x + mb)/(x - mb)`
If `(x^2 - 4)/(x^2 + 4) = 3/5`, the value of x is ______.
